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chapter 11
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Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce thematerial contained herein on the condition that such material be reproduced only forclassroom use; be provided to students, teacher, and families without charge; andbe used solely in conjunction with Glencoe Mathematics: Applications andConcepts, Course 2. Any other reproduction, for use or sale, is prohibited withoutprior written permission of the publisher.
Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240
Mathematics: Applications and Concepts, Course 2ISBN: 0-07-860118-5 Chapter 11 Resource Masters
2 3 4 5 6 7 8 9 10 047 12 11 10 09 08 07 06 05 04
Consumable Workbooks Many of the worksheets contained in the ChapterResource Masters booklets are available as consumable workbooks in bothEnglish and Spanish.
Study Guide and Intervention Workbook 0-07-860128-2
Study Guide and Intervention Workbook (Spanish) 0-07-860134-7
Practice: Skills Workbook 0-07-860129-0
Practice: Skills Workbook (Spanish) 0-07-860135-5
Practice: Word Problems Workbook 0-07-860130-4
Practice: Word Problems Workbook (Spanish) 0-07-860136-3
Answers for Workbooks The answers for Chapter 11 of theseworkbooks can be found in the back of this Chapter Resource Mastersbooklet.
StudentWorks™ This CD-ROM includes the entire Student Edition textalong with the English workbooks listed above.
TeacherWorks™ All of the materials found in this booklet are includedfor viewing and printing in the Glencoe Mathematics: Applications andConcepts, Course 2 TeacherWorks™ CD-ROM.
Spanish Assessment Masters Spanish versions of forms 2A and 2C ofthe Chapter 11 Test are available in the Glencoe Mathematics: Applicationsand Concepts Spanish Assessment Masters, Course 2 (0-07-860138-X).
iii
Vocabulary Builder .............................vii
Family Letter............................................ix
Family Activity ........................................x
Lesson 11-1Study Guide and Intervention ........................609Practice: Skills ................................................610Practice: Word Problems................................611Reading to Learn Mathematics......................612Enrichment .....................................................613
Lesson 11-2Study Guide and Intervention ........................614Practice: Skills ................................................615Practice: Word Problems................................616Reading to Learn Mathematics......................617Enrichment .....................................................618
Lesson 11-3Study Guide and Intervention ........................619Practice: Skills ................................................620Practice: Word Problems................................621Reading to Learn Mathematics......................622Enrichment .....................................................623
Lesson 11-4Study Guide and Intervention ........................624Practice: Skills ................................................625Practice: Word Problems................................626Reading to Learn Mathematics......................627Enrichment .....................................................628
Lesson 11-5Study Guide and Intervention ........................629Practice: Skills ................................................630Practice: Word Problems................................631Reading to Learn Mathematics......................632Enrichment .....................................................633
Lesson 11-6Study Guide and Intervention ........................634Practice: Skills ................................................635Practice: Word Problems................................636Reading to Learn Mathematics......................637Enrichment .....................................................638
Lesson 11-7Study Guide and Intervention ........................639Practice: Skills ................................................640Practice: Word Problems................................641Reading to Learn Mathematics......................642Enrichment .....................................................643
Lesson 11-8Study Guide and Intervention ........................644Practice: Skills ................................................645Practice: Word Problems................................646Reading to Learn Mathematics......................647Enrichment .....................................................648
Chapter 11 AssessmentChapter 11 Test, Form 1 ........................649–650Chapter 11 Test, Form 2A......................651–652Chapter 11 Test, Form 2B......................653–654Chapter 11 Test, Form 2C......................655–656Chapter 11 Test, Form 2D......................657–658Chapter 11 Test, Form 3 ........................659–660Chapter 11 Extended Response
Assessment ...............................................661Chapter 11 Vocabulary Test/Review...............662Chapter 11 Quizzes 1 & 2..............................663Chapter 11 Quizzes 3 & 4..............................664Chapter 11 Mid-Chapter Test .........................665Chapter 11 Cumulative Review......................666Chapter 11 Standardized Test Practice..667–668
Standardized Test Practice Student Recording Sheet ..............................A1
Standardized Test Practice Rubric...................A2ANSWERS .............................................A3–A32
CONTENTS
iv
Teacher’s Guide to Using the Chapter 11 Resource Masters
The Fast File Chapter Resource system allows you to conveniently file the resources youuse most often. The Chapter 11 Resource Masters includes the core materials needed forChapter 11. These materials include worksheets, extensions, and assessment options. Theanswers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing in theGlencoe Mathematics: Applications and Concepts, Course 2, TeacherWorks CD-ROM.
Vocabulary Builder Pages vii-viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.
When to Use Give these pages to studentsbefore beginning Lesson 11-1. Encouragethem to add these pages to theirmathematics study notebook. Remind themto add definitions and examples as theycomplete each lesson.
Family Letter and Family ActivityPage ix is a letter to inform your students’families of the requirements of the chapter.The family activity on page x helps themunderstand how the mathematics studentsare learning is applicable to real life.
When to Use Give these pages to studentsto take home before beginning the chapter.
Study Guide and InterventionThere is one Study Guide and Interventionmaster for each lesson in Chapter 11.
When to Use Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.
Practice: Skills There is one master foreach lesson. These provide practice thatmore closely follows the structure of thePractice and Applications section of theStudent Edition exercises.
When to Use These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.
Practice: Word Problems There is onemaster for each lesson. These providepractice in solving word problems that applythe concepts of the lesson.
When to Use These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.
Reading to Learn Mathematics Onemaster is included for each lesson. The firstsection of each master asks questions aboutthe opening paragraph of the lesson in theStudent Edition. Additional questions askstudents to interpret the context of andrelationships among terms in the lesson.Finally, students are asked to summarizewhat they have learned using variousrepresentation techniques.
When to Use This master can be used as astudy tool when presenting the lesson or asan informal reading assessment afterpresenting the lesson. It is also a helpful toolfor ELL (English Language Learner)students.
v
Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.
When to Use These may be used as extracredit, short-term projects, or as activitiesfor days when class periods are shortened.
Assessment OptionsThe assessment masters in the Chapter 11Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.
Chapter AssessmentChapter Tests
• Form 1 contains multiple-choice questionsand is intended for use with basic levelstudents.
• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.
• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.
• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.
All of the above tests include a free-responseBonus question.
• The Extended-Response Assessmentincludes performance assessment tasksthat are suitable for all students. Ascoring rubric is included for evaluationguidelines. Sample answers are providedfor assessment.
• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used inconjunction with one of the chapter testsor as a review worksheet.
Intermediate Assessment• Four free-response quizzes are included
to offer assessment at appropriateintervals in the chapter.
• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice and free-response questions.
Continuing Assessment• The Cumulative Review provides
students an opportunity to reinforce andretain skills as they proceed through theirstudy of Glencoe Mathematics:Applications and Concepts, Course 2. Itcan also be used as a test. This masterincludes free-response questions.
• The Standardized Test Practice offerscontinuing review of pre-algebra conceptsin various formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, short response, grid-in, andextended response questions. Bubble-inand grid-in answer sections are providedon the master.
Answers• Page A1 is an answer sheet for the
Standardized Test Practice questions thatappear in the Student Edition on pages 508–509. This improves students’familiarity with the answer formats theymay encounter in test taking.
• Detailed rubrics for assessing theextended response questions on page 509are provided on page A2.
• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.
• Full-size answer keys are provided for theassessment masters in this booklet.
© Glencoe/McGraw-Hill vii Mathematics: Applications and Concepts, Course 2
This is an alphabetical list of new vocabulary terms you will learn inChapter 11. As you study the chapter, complete each term’s definitionor description. Remember to add the page number where you foundthe term. Add these pages to your math study notebook to reviewvocabulary at the end of the chapter.
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn MathematicsVocabulary Builder
Vocabulary TermFound
Definition/Description/Exampleon Page
base
complex figure
height
hypotenuse[heye-PAH-tuhn-OOS]
irrational number
Vo
cab
ula
ry B
uild
er
Vocabulary TermFound
Definition/Description/Exampleon Page
leg
perfect square
Pythagorean[puh-THAG-uh-REE-uhn] Theorem
radical sign
square
square roots
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn MathematicsVocabulary Builder (continued)
© Glencoe/McGraw-Hill viii Mathematics: Applications and Concepts, Course 2
© Glencoe/McGraw-Hill ix Mathematics: Applications and Concepts, Course 2
Family LetterNAME ________________________________________ DATE ______________ PERIOD _____
Dear Parent or Guardian:
We use math skills in many of the things that we do. One of
the goals of this class is to show students how things they are
learning in the classroom are relevant to the real world. For
example, understanding area is useful in such diverse fields as
geography, navigation, sports, and architecture.
In Chapter 11, Geometry: Measuring Two-Dimensional
Figures, your child will learn how to find squares and square
roots, use the Pythagorean Theorem, and find areas of figures.
In the study of this chapter, your child will complete a variety of
daily classroom assignments and activities and possibly produce
a chapter project.
By signing this letter and returning it with your child, you agree
to encourage your child by getting involved. Enclosed is an
activity you can do with your child that also relates the math in
Chapter 11 to the real world. You may also wish to log on to
the Online Study Tools for self-check quizzes, Parent and
Student Study Guide pages, and other study help at
www.msmath2.net. If you have any questions or comments, feel
free to contact me at school.
Sincerely,
Fam
ily L
ette
r
Signature of Parent or Guardian ______________________________________ Date ________
© Glencoe/McGraw-Hill x Mathematics: Applications and Concepts, Course 2
Family ActivityNAME ________________________________________ DATE ______________ PERIOD _____
Estimating AreasWith a family member, find four small objects around the house. Puteach one on the centimeter grid and draw an outline of one side ofthe object. Estimate the area of the outline.
1. name of object: 2. name of object:
3. name of object: 4. name of object:
5. Choose one of your objects. Give a reason why you might want to find thearea of the object. Work with your family member to get ideas.
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© Glencoe/McGraw-Hill 609 Mathematics: Applications and Concepts, Course 2
a. Find the square of 5. Find the square of 16.
5 � 5 � 25 16 256
a. Find �49�. Find �169�.
7 � 7 � 49, so �49� � 7. 169 13
So, �169� � 13.
A square tile has an area of 144 square inches. What are thedimensions of the tile?
144 12 Find the square root of 144.
So, the tile measures 12 inches by 12 inches.
Find the square of each number.
1. 2 2. 9 3. 14
4. 15 5. 21 6. 45
Find each square root.
7. �16� 8. �36� 9. �256�
10. �1,024� 11. �361� 12. �484�
ENTER2nd
ENTER2nd
ENTER
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionSquares and Square Roots
The product of a number and itself is the square of the number. Numbers like 4, 25, and 2.25 arecalled perfect squares because they are squares of rational numbers. The factors multiplied to formperfect squares are called square roots. Both 5 � 5 and (�5)(�5) equal 25. So, 25 has two squareroots, 5 and �5. A radical sign, ��, is the symbol used to indicate the positive square root of anumber. So, �25� � 5.
Find the square of each number.
1. 3 2. 22
3. 25 4. 24
5. 35 6. 26
7. 37 8. 50
Find each square root.
9. �25� 10. �100�
11. �441� 12. �900�
13. �961� 14. �784�
15. �3,600� 16. �1,936�
17. What is the square of �37? 18. Find both square roots of 4,900.
19. Square 7.2. 20. Square 4.5.
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: SkillsSquares and Square Roots
© Glencoe/McGraw-Hill 610 Mathematics: Applications and Concepts, Course 2
© Glencoe/McGraw-Hill 611 Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Word ProblemsSquares and Square Roots
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1. FERTILIZER John bought a bag of lawnfertilizer that will cover 400 squarefeet. What are the dimensions of thelargest square plot of lawn that the bagof fertilizer will cover?
2. GEOMETRY The area A of a circle insquare feet with a radius r in feet isgiven approximately by the formulaA � 3.14r2. What is the approximatearea of a circle with a radius of 3 feet?
3. MOTION The time t in seconds for anobject dropped from a height of h feetto hit the ground is given by the
formula t � ��23h2��. How long will it take
an object dropped from a height of 500 feet to hit the ground? Round tothe nearest tenth.
4. PACKAGING A cardboard envelope for acompact disc is a square with an areaof 171.61 square centimeters. What arethe dimensions of the envelope?
5. GEOGRAPHY Refer to the squaresbelow. They represent the approximateareas of California, Alabama, andNebraska. Find the area of Alabama.
277 mi
225 mi
395 mi
AL
NE
CA
6. Use the figure in Exercise 5. How muchlarger is California than Nebraska?
© Glencoe/McGraw-Hill 612 Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
Pre-Activity Complete the Mini Lab at the top of page 470 in your textbook.Write your answers below.
1. On grid paper, draw and label three other rectangles that have a perimeter of 16 units.
2. Summarize the dimensions and areas of the rectangles that you drew in a table like the one shown below.
3. Draw three different rectangles that have a perimeter of12 units and find their areas.
4. What do you notice about the rectangles with the greatest areas?
Reading the Lesson 5. In this lesson, the word square is used in several different ways. Tell the
meaning of the word as it is used in each phrase or sentence.a. Find the square of 3.
b. 9 units squared
c. A boxing ring is a square with an area of 400 ft2.
Helping You Remember6. Work with a partner. Use a calculator to find the squares of six numbers,
some of them decimals. Then write only the squares in a list andexchange lists with your partner. Find the square roots of the squares inthe list that you receive. Write your answers in the form �x� � y.
5 units1 unit
4 units2 units
3 units
3 units
5 square units8 square units
9 square units
2 � 6 12
16
3 � 5
4 � 4
15
1 � 7 7
Drawing Dimensions (units) Area (sq units)
6 units
2 units
5 units
3 units
4 units
4 units
Reading to Learn MathematicsSquares and Square Roots
© Glencoe/McGraw-Hill 613 Mathematics: Applications and Concepts, Course 2
The Geometric MeanThe square root of the product of two numbers is called their geometric mean.The geometric mean of 12 and 48 is �12 � 4�8� � �576� or 24.
Find the geometric mean for each pair of numbers.
1. 2 and 8 2. 4 and 9 3. 9 and 16
4. 16 and 4 5. 16 and 36 6. 12 and 3
7. 18 and 8 8. 2 and 18 9. 27 and 12
Recall the definition of a geometric sequence. Each term is found bymultiplying the previous term by the same number. A missing term in ageometric sequence equals the geometric mean of the two terms on eitherside.
Find the missing term in each geometric sequence.
10. 4, 12, , 108, 324 11. 10, , 62.5, 156.25, 390.625
12. 1, 0.4, , 0.064, 0.0256 13. 700, 70, 7, 0.7, , 0.007
14. 6, , 24 15. 18, , 32??
??
??
EnrichmentNAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
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© Glencoe/McGraw-Hill 614 Mathematics: Applications and Concepts, Course 2
Estimate �40� to the nearest whole number.
List some perfect squares.
1, 4, 9, 16, 25, 36, 49, …
36 � 40 � 49 40 is between the perfect squares 36 and 49.
�36� � �40� � �49� Find the square root of each number.
6 � �40� � 7 �36� � 6 and �49� � 7
So, �40� is between 6 and 7. Since 40 is closer to 36 than to 49, the best whole numberestimate is 6.
Use a calculator to find the value of �28� tothe nearest tenth.
28 5.291502622
�28� � 5.3
Check Since 52 � 25 and 25 is close to 28, the answer is reasonable.
Estimate each square root to the nearest whole number.
1. �3� 2. �8�
3. �26� 4. �41�
5. �61� 6. �94�
7. �152� 8. �850�
Use a calculator to find each square root to the nearest tenth.
9. �2� 10. �27�
11. �73� 12. �82�
13. �105� 14. �395�
15. �846� 16. �2,298�
ENTER2nd
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionEstimating Square Roots
Recall that a perfect square is a square of a rational number. In Lesson 5-8, you learned that anynumber that can be written as a fraction is a rational number. A number that cannot be written as afraction is an irrational number.
0 1 2 3 4 5 6
28
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© Glencoe/McGraw-Hill 615 Mathematics: Applications and Concepts, Course 2
Estimate each square root to the nearest whole number.
1. �5� 2. �10� 3. �21�
4. �28� 5. �78� 6. �102�
7. �179� 8. �274� 9. �303�
10. �563� 11. �592� 12. �755�
13. �981� 14. �1,356� 15. �1,688�
16. �3,287� 17. �3,985� 18. �4,125�
Use a calculator to find each square root to the nearest tenth.
19. �6� 20. �19� 21. �30�
22. �77� 23. �114� 24. �125�
25. �149� 26. �182� 27. �212�
28. �436� 29. �621� 30. �853�
31. �918� 32. �1,004� 33. �1,270�
34. �5,438� 35. �4,215� 36. �5,786�
37. Order �275�, 4.91, and �23� from least to greatest.
38. Graph �42� and �62� on the same number line.
0 1 2 3 4 5 876
Practice: SkillsEstimating Square Roots
NAME ________________________________________ DATE ______________ PERIOD _____
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Word ProblemsEstimating Square Roots
© Glencoe/McGraw-Hill 616 Mathematics: Applications and Concepts, Course 2
1. GEOMETRY The diameter d of a circlewith area A is given by the formula
d � ��4�A��. What is the diameter of a
circle with an area of 56 square inches?Use 3.14 for � and round to the nearesttenth.
2. FENCING Carmen wants to buy fencingto enclose a square garden with anarea of 500 square feet. How muchfencing does Carmen need to buy?Round to the nearest tenth.
3. OCEANS The speed v in feet per secondof an ocean wave in shallow water ofdepth d in feet is given by the formulav � �32d�. What is the speed of anocean wave at a depth of 10 feet?Round to the nearest tenth.
4. LIGHTING A new flashlight has a beamwhose width w at a distance d from theflashlight is given by the formulaw � 1.2�d�. What is the width of thebeam at a distance of 30 feet? Round tothe nearest tenth.
5. SOUND The speed of sound in air c inmeters per second at a temperature Tin degrees Celsius is givenapproximately by the formula c � �402(T�� 273�)�. What is the speedof sound in air at a temperature of 25 degrees Celsius? Round to thenearest tenth.
6. PROJECTILES The muzzle velocity v infeet per second necessary for a cannonto hit a target x feet away is estimatedby the formula v � �32x�. What muzzlevelocity is required to hit a target3,000 feet away? Round to the nearesttenth.
3,000 ft
© Glencoe/McGraw-Hill 617 Mathematics: Applications and Concepts, Course 2
Pre-Activity Complete the Mini Lab at the top of page 475 in your textbook.Write your answers below.Use algebra tiles to estimate the square root of each number tothe nearest whole number.
1. 40 2. 28 3. 85 4. 62
5. Describe another method that you could use to estimate the square rootof a number.
Reading the Lesson
6. Why is �4� a rational number and �2� an irrational number?
7. How do you read the statement �64� � �75� � �81�?
8. Why are �64� and �81� used in Example 1?
Helping You Remember9. The key to estimating square roots without a calculator is to be familiar
with common perfect squares. Complete the following table of commonperfect squares then test yourself to see how many you can rememberwithout using a calculator.
Reading to Learn MathematicsEstimating Square Roots
NAME ________________________________________ DATE ______________ PERIOD _____
Number 5 6 7 8 9 10 11 12 13 14 15 16 20 25
Square 25
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World Series RecordsEach problem gives the name of a famous baseball player. To findwho set each record, graph the points on the number line.
1. pitched 23 strikeouts in one World Series
U at �3�, X at 3.3, K at 0.75, O at �32�, F at �6�, A at 2�
78�
2. 71 base hits in his appearances in World Series
B at �5�, R at �12�, A at 3.75, G at �1163�
, E at �52�, Y at 0.375, R at �
143�,
I at 1.6, and O at 0.7�
3. 10 runs in a single World Series
N at �60�, K at �30�, A at 4.3, S at 6.2, C at �496�, O at �45�, and J at �17�
4. batting average of 0.625 in a single World Series
E at �32�, U at 6�56�, A at �
134�, T at �55�, B at 5.3, R at �40�, H at 7.75,
B at �251�
5. 42 World Series runs in his career
E at �140�, Y at 9.6, I at 8.6, E at �90�, A at �221�, M at �70�, C at 8�
78�,
M at �100�, N at 10.7, K at 9�111�
, T at �120�, L at 11.4
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
© Glencoe/McGraw-Hill 618 Mathematics: Applications and Concepts, Course 2
0 4321
4 8765
0 4321
4 8765
8 1211109
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© Glencoe/McGraw-Hill 619 Mathematics: Applications and Concepts, Course 2
Find the missing measure of a right triangle if a � 4 inches and b � 3 inches.
c2 � a2 � b2 Pythagorean Theorem
c2 � 42 � 32 Replace a with 4 and b with 3.
c2 � 16 � 9 Evaluate 42 and 32.
c2 � 25 Add.
�c2� � �25� Take the square root of each side.
c � 5 Simplify.
The length of the hypotenuse is 5 inches.
Determine whether a triangle with side lengths of 6 meters,9 meters, and 12 meters is a right triangle.
c2 � a2 � b2 Pythagorean Theorem
122 � 62 � 92 Replace a with 6, b with 9, and c with 12.
144 � 36 � 81 Simplify.
144 117 Add.
The triangle is not a right triangle.
Find the missing measure of each right triangle. Round to the nearesttenth if necessary.
1. 2. 3.
Determine whether each triangle with the given side lengths is aright triangle. Write yes or no.
4. 15 ft, 8 ft, 17 ft 5. 5 in., 13 in., 17 in. 6. 9 yd, 40 yd, 41 yd
13 cm
16 cm
a cm5 m
7.5 m
c m
9 in.
4 in.c in.
3 in.
4 in.c in.
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionThe Pythagorean Theorem
The sides of a right triangle have special names. The sides adjacent to the right angle are the legs. The side opposite the right angle is the c2 � a2 � b2
hypotenuse. The Pythagorean Theorem describes the relationship between the length of the hypotenuse and the lengths of the legs. In a right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs.
b
ac
Find the missing measure of each right triangle. Round to the nearesttenth if necessary.
1. 2.
3. 4.
5. 6.
7. 8.
9. a � 15 cm, b � 20 cm 10. a � 2 yd, b � 12 yd
11. a � 13 in., c � 16.5 in. 12. b � 8 mm, c � 17 mm
13. a � 1.3 ft, b � 4.6 ft 14. a � 14.7 m, c � 23 m
Determine whether each triangle with the given side lengths is aright triangle. Write yes or no.
15. 10 ft, 24 ft, 26 ft 16. 5 in., 8 in., 9 in.
17. 6 cm, 9 cm, 12 cm 18. 4.5 mm, 6.0 mm, 7.5 mm
14 mmc mm
6.7 mm
11.2 m
6 m
a m
2.7 yd 3 yd
a yd
20.3 in. 32 in.
c in.
20 cm
26 cmx cm12.4 ft
a ft
15 ft
5 in.
c in.
5 in.7 m
b m
20 m
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: SkillsThe Pythagorean Theorem
© Glencoe/McGraw-Hill 620 Mathematics: Applications and Concepts, Course 2
© Glencoe/McGraw-Hill 621 Mathematics: Applications and Concepts, Course 2
Practice: Word ProblemsThe Pythagorean Theorem
NAME ________________________________________ DATE ______________ PERIOD _____
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1. ORIGAMI Chee has a piece of papermeasuring 8.5 inches by 8.5 inches. Ifshe folds the paper diagonally in half,how long is the folded side? Round tothe nearest tenth.
2. COMPUTERS In a computer catalog,a computer monitor is said to be 19 inches. This distance is the diagonaldistance across the screen. If the screenis 10 inches high, what is the width ofthe screen? Round to the nearest tenth.
3. ANTENNAS A wire 10 meters long issupporting a utility pole. The wire isanchored to the ground and is attachedto the pole 9 meters above the ground.What is the distance from the bottom ofthe pole to the point where the wire isattached to the ground? Round to thenearest tenth.
9 m10 m
x m
4. RAMPS Crystal wants to build a rampthat will rise 4 feet over a horizontaldistance of 20 feet. How long will theramp be? Round to the nearest tenth.
4 ft
20 ft
x ft
5. POOLS Salomon swims diagonallyacross his pool every day. If Salomon’spool is 4 meters wide and 16 metersdiagonally across, how long is his pool,to the nearest tenth of a meter?
6. FRAMES Rosa has a picture frame thatmeasures 12 inches by 18 inches. Whatis the diagonal distance across theframe? Round to the nearest tenth.
Pre-Activity Read the introduction at the top of page 479 in your textbook.Write your answers below.
1. Can the mirror fit through the doorway? Explain.
2. Make a scale drawing on grid paper to solve the problem.
Reading the Lesson3. In the Pythagorean Theorem c2 � a2 � b2, which letter represents
the length of the hypotenuse?
4. How do you know that the diagonal of a rectangle is the hypotenuse oftwo right triangles?
5. In Examples 4 and 5 on page 481, how do you know which length is c?
Helping You Remember6. Summarize what you learned in this lesson by labeling the sides of the
right triangle with the letters a, b, and c and then completing the table.
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn MathematicsThe Pythagorean Theorem
© Glencoe/McGraw-Hill 622 Mathematics: Applications and Concepts, Course 2
You canfind
If you knowthe lengths
a
b
c
© Glencoe/McGraw-Hill 623 Mathematics: Applications and Concepts, Course 2
Pythagoras in the AirIn the diagram at the right, an airplane heads north at 180 mi/h.But, the wind is blowing towards the east at 30 mi/h. So, theairplane is really traveling east of north. The middle arrow in thediagram shows the actual direction of the airplane.
The actual speed of the plane can be found using the PythagoreanTheorem.
�302 �� 1802� � �900 �� 32,40�0�
� �33,30�0�
� 182.5
The plane’s actual speed is about 182.5 mi/h.
Find the actual speed of each airplane. Round answers to the nearesttenth. (You might wish to draw a diagram to help you solve theproblem.)
1. An airplane travels at 240 mi/h east. 2. An airplane travels at 620 mi/h west.A wind is blowing at 20 mi/h toward A wind is blowing at 35 mi/h towardthe south. the south.
3. An airplane travels at 450 mi/h south. 4. An airplane travels at 1,200 mi/h east.A wind is blowing at 40 mi/h toward A wind is blowing at 30 mi/h towardthe east. the north.
EnrichmentNAME ________________________________________ DATE ______________ PERIOD _____
E
N(not drawn to scale)
180 mi/h
30 mi/h
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© Glencoe/McGraw-Hill 624 Mathematics: Applications and Concepts, Course 2
Find the area of a parallelogram if the base is 6 inches and the height is 3.7 inches.
Estimate A � 6 � 4 or 24 in2
A � bh Area of a parallelogram
A � 6 � 3.7 Replace b with 6 and h with 3.7.
A � 22.2 Multiply.
The area of the parallelogram is 22.2 square inches. This is close to the estimate.
Find the area of the parallelogram at the right.
Estimate A � 10 � 10 or 100 cm2
A � bh Area of a parallelogram
A � 12 � 8 Replace b with 12 and h with 8.
A � 96 Multiply.
The area of the parallelogram is 96 square centimeters. This is close to the estimate.
Find the area of each parallelogram. Round to the nearest tenth ifnecessary.
1. 2. 3. 17 in.
16 in.
4.6 mm
8 mm
5 ft
13.2 ft
12 cm
8 cm
3.7 in.
6 in.
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionArea of Parallelograms
The area A of a parallelogram equals the product of its base b and its height h.
A � bh
The base is any side of a parallelogram.
The height is the length ofthe segment perpendicularto the base with endpointson opposite sides.
b
h
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© Glencoe/McGraw-Hill 625 Mathematics: Applications and Concepts, Course 2
Find the area of each parallelogram. Round to the nearest tenth ifnecessary.
1. base � 5 ft 2. base � 9 in.height � 12 ft height � 2 in.
3. base � 6 cm 4. base � 4�25� yd
height � 5.5 cm height � 2 yd
5. base � 15.3 mm 6. base � 19.6 mheight � 8 mm height � 14.5 m
7. 8.
9. 10.
11. 12.
13. 14.
7 yd
24 ft
4.3 mm
12 mm
20 in.
11 in.45
2.3 cm
2 cm
12 ft
9 ft15 mm
11 mm
7 in.
4 in.
2 cm
3 cm
Practice: SkillsArea of Parallelograms
NAME ________________________________________ DATE ______________ PERIOD _____
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Word ProblemsArea of Parallelograms
© Glencoe/McGraw-Hill 626 Mathematics: Applications and Concepts, Course 2
1. SAILS Joyce wants to construct a sailwith the dimensions shown. How muchmaterial will be used?
14 ft
25 ft
2. SIGNS Pedro wants to make the sign inthe shape shown and needs to knowhow much material will be needed.What is the area of the sign?
30 in.
35 in.
YardSale
3. SHADING Alma’s engineering firm mustdetermine the area of the largestnoontime shadow that a proposedbuilding design will create. What is thearea of the shadow?
40 ft
56 ft
4. POOLS Tamika has designed a pool inthe shape shown. What is the area ofthe bottom of the pool if the surface isperfectly flat?
30 m20 m
5. CITY PLANNING Two parallel streets arecut across by two other parallel streetsas shown in the figure, cutting off aparcel of land in the shape of aparallelogram. Find the area of theparcel of land.
250 ft
340 ft
Main Street
Dresden Way
Colu
mbu
s Av
e.
Jeffe
rson
Ave
.
6. TARPS Neka wants to cut a tarp in theshape shown. What is the minimumamount of canvas cloth that he willneed?
36 ft
40 ft
© Glencoe/McGraw-Hill 627 Mathematics: Applications and Concepts, Course 2
Pre-Activity Complete the Mini Lab at the top of page 483 in your textbook.Write your answers below.
1. What is the value of x and y for each parallelogram?
2. Count the grid squares to find the area of each parallelogram.
3. On grid paper, draw three different parallelograms in which x � 5 unitsand y � 4 units. Find the area of each.
4. Make a conjecture about how to find the area of a parallelogram if youknow the values of x and y.
Reading the Lesson5. Explain how to find the height of a parallelogram.
6. Suppose you are asked to find the area of the parallelogram below. Is thegiven solution correct? Explain.
A � bhA � 12 � 5A � 60The area of the parallelogram is 60 square centimeters.
Helping You Remember7. Because rectangles, rhombuses, and squares are all parallelograms, the
formula for finding the area of a parallelogram is also used to find theareas of each of these figures. Think of a way to remember that the areaof a parallelogram is the product of its base and height. For example,draw several parallelograms, rectangles, rhombuses, and squares andlabel the base and height for each. Write the formula for the area beloweach model.
3 cm5 cm
12 cm
Reading to Learn MathematicsArea of Parallelograms
NAME ________________________________________ DATE ______________ PERIOD _____
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Two Area PuzzlesCut out the five puzzle pieces at the bottom of this page. Then usethem to solve these two puzzles.
1. Use all five puzzle pieces to make 2. Use the four largest pieces to makea square with an area of 9 square a square with an area of 8 squareinches. Record your solution below. inches. Record your solution below.
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
© Glencoe/McGraw-Hill 628 Mathematics: Applications and Concepts, Course 2
2 in.
1 in.
1 in.
2 in.
2 in.
1 in2
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© Glencoe/McGraw-Hill 629 Mathematics: Applications and Concepts, Course 2
Find the area of the triangle.Estimate �
12
�(6)(5) � 15
A � �12�bh Area of a triangle
A � �12�6 � 4.5 Replace b with 6 and h with 4.5.
A � 13.5 Multiply.
The area of the triangle is 13.5 square inches. This is close to the estimate.
Find the area of the trapezoid.
A � �12�h(b1 � b2) Area of a trapezoid
A � �12�(4)(3 � 6) Replace h with 4, b1 with 3, and b2 with 6.
A � 18 Simplify.
The area of the trapezoid is 18 square centimeters.
Find the area of each figure. Round to the nearest tenth if necessary.
1. 2. 3. 4. 8 cm
13.5 cm
18 cm
7 in.
5 in.
14 in.
7 mm
9 mm12 ft
7 ft
4 cm
3 cm
6 cm
4.5 in.
6 in.
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionArea of Triangles and Trapezoids
The area A of a triangle equals half the product of its base b and its height h.
A � �12�bh
A trapezoid has two bases, b1 and b2. The height of a trapezoid is the distance between the two bases. The area A of a trapezoid equals half the product of the height h and the sum of the bases b1 and b2.
A � �12�h(b1 � b2)
b1
b2
h
The base of atriangle can beany of its sides.
The height is thedistance from a baseto the opposite vertex.
b
h
Find the area of each figure. Round to the nearest tenth if necessary.
1. 2.
3. 4.
5. 6.
7. 8.
9. 10.
11. triangle: base � 16 cm, height � 9.4 cm
12. triangle: base � 13.5 in., height � 6.4 in.
13. trapezoid: bases 22.8 mm and 19.7 mm, height 36 mm
14. trapezoid: bases 5 ft and 3�12� yd, height 7 ft
14 mm
3.8 mm
15.3 mm
7.5 cm
12.2 cm
5.6 in.
6.9 in.12 ft
20.1 ft
25 ft
24 mm
20.7 mm7 cm
9.2 cm
2 cm
4 ft
3 ft
6.5 ft
12 mm
18 mm
10 mm
3 ft
2 ft10 cm
9 cm
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: SkillsArea of Triangles and Trapezoids
© Glencoe/McGraw-Hill 630 Mathematics: Applications and Concepts, Course 2
© Glencoe/McGraw-Hill 631 Mathematics: Applications and Concepts, Course 2
Practice: Word ProblemsArea of Triangles and Trapezoids
NAME ________________________________________ DATE ______________ PERIOD _____
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51. GEOGRAPHY Arkansas has a shape thatis similar to a trapezoid with bases ofabout 182 miles and 267 miles and aheight of about 254 miles. Estimate thearea of the state.
2. PATIOS Greta is making a patio withthe dimensions given in the figure.What is the area of the patio?
172.5 ft2
15 ft
15 ft
8 ft
3. FLAGS Malila wants to make theInternational Marine Signal flag shownwhich represents the number six. Whatis the area of the flag?
30 in.100 in. 5 in.
4. SIGNS Estimate the area of the yieldsign.
390 in2
30 in.
26 in.
5. TILING A ceramics company wants toproduce tiles in the shape shown. Whatis the area of the surface of each tile?
8.5 cm
8.5 cm
6. GARDENING Kinu wants to buy topsoilfor a section of her garden that has thedimensions shown in the figure. Whatis the area of this section of Kinu’sgarden?
7 yd2
4 yd
3.5 yd
4 yd
Pre-Activity Complete the Mini Lab at the top of page 489 in your textbook.Write your answers below.
1. What is the area of the parallelogram?
2. Cut along the diagonal. What is true about the triangles formed?
3. What is the area of each triangle?
4. If the area of a parallelogram is bh, then write an expression for the areaA of each of the two congruent triangles that form the parallelogram.
Reading the Lesson5. In a triangle, which side is the base?
6. How do you find the height of a triangle?
7. For what kind of triangle might the height be found outside of thetriangle?
8. How is the height of a trapezoid similar to the height of a triangle orparallelogram?
Helping You Remember9. The Mini Lab in this lesson gave you a good way to remember the
formula for the area of a triangle by showing you that it is half the areaof a parallelogram, so A � �
12�bh. Think of a way to help you remember the
formula for the area of a trapezoid. Do you recognize anything in the
formula A � �12�h(b1 � b2)?
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn MathematicsArea of Triangles and Trapezoids
© Glencoe/McGraw-Hill 632 Mathematics: Applications and Concepts, Course 2
© Glencoe/McGraw-Hill 633 Mathematics: Applications and Concepts, Course 2
Heron’s FormulaA formula named after Heron of Alexandria, Egypt, can be used to findthe area of a triangle given the lengths of its sides.
Heron’s formula states that the area A of a triangle whose sides measurea, b, and c is given by
A � �s(s�a�)(s�b)�(s�c)�,
where s is the semiperimeter:
s � �a �
2b � c�.
Estimate the area of each triangle by finding the mean of the innerand outer measures. Then use Heron’s Formula to compute a moreexact area. Give each answer to the nearest tenth of a square unit.
1. 2. 3.
Estimated area: Estimated area: Estimated area:
Computed area: Computed area: Computed area:
4. 5. 6.
Estimated area: Estimated area: Estimated area:
Computed area: Computed area: Computed area:
9
57
8
83
7
77
6
8
109
9
106
66
EnrichmentNAME ________________________________________ DATE ______________ PERIOD _____
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© Glencoe/McGraw-Hill 634 Mathematics: Applications and Concepts, Course 2
Find the area of the circle.
A � �r2 Area of circle
A � � � 52 Replace r with 5.
5 78.53981634
The area of the circle is approximately 78.5 square centimeters.
Find the area of a circle that has a diameter of 9.4 millimeters.
A � �r2 Area of a circle
A � � � 4.72 Replace r with 9.4 2 or 4.7.
A � 69.4 Use a calculator.
The area of the circle is approximately 69.4 square millimeters.
Find the area of each circle. Round to the nearest tenth.
1. 2. 3.
4. radius � 2.6 cm 5. radius � 14.3 in. 6. diameter � 5�12� yd
7. diameter � 4�34
� mi 8. diameter � 7.9 mm 9. radius � 2�15� ft
12 ft
25 mm7 in.
ENTER��
5 cm
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionArea of Circles
The area A of a circle equals the product of pi (�) and the square of its radius r.
A � �r 2
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© Glencoe/McGraw-Hill 635 Mathematics: Applications and Concepts, Course 2
Find the area of each circle. Round to the nearest tenth.
1. 2.
3. 4.
5. 6.
7. 8.
9. 10.
11. radius � 5.7 mm 12. radius � 8.2 ft
13. diameter � 3�14� in. 14. diameter � 15.6 cm
15. radius � 1.1 in. 16. diameter � 12�34� yd
11.9 ft2.1 mm
22.5 in.
4.7 yd
8 cm4.3 ft
14 in.35 mm
4 yd
1 cm
Practice: SkillsArea of Circles
NAME ________________________________________ DATE ______________ PERIOD _____
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Word ProblemsArea of Circles
© Glencoe/McGraw-Hill 636 Mathematics: Applications and Concepts, Course 2
1. POOLS Susan designed a circular poolwith a diameter of 25 meters. What isthe area of the bottom of the pool?Round to the nearest tenth.
2. MONEY Find the area of the coin to thenearest tenth.
19 mm
3. DRUMS What is the area of thedrumhead on the drum shown below?Round to the nearest tenth.
14 in.
4. PIZZA Estimate the area of the top of around pizza that has a diameter of16 inches. Round to the nearest tenth.
5. GARDENING Jane needs to buy mulchfor the garden with the dimensionsshown in the figure. For how much areadoes Jane need to buy mulch? Round tothe nearest tenth.
5.5 yd
6. UTILITIES What is the area of the topsurface of a circular manhole cover thathas a radius of 30 centimeters? Roundto the nearest tenth.
© Glencoe/McGraw-Hill 637 Mathematics: Applications and Concepts, Course 2
Pre-Activity Complete the Mini Lab at the top of page 493 in your textbook.Write your answers below.
1. What is the measurement of the base and the height?
2. Substitute these values into the formula for the area of a parallelogram.
3. Replace C with the expression for the circumference of a circle, 2�r.Simplify the equation and describe what it represents.
Reading the Lesson4. The formula for the area of a circle uses the number �. How does this
affect the value of the area of a circle found using the formula?
5. If you are given the length of the diameter of a circle, how can you find itsarea?
Helping You Remember6. Think about the formulas you have learned that involve circles: C � 2�r
or C � �d and A � �r2. To help you remember the difference between theformulas for circumference and the formula for area, think about thedifferences in the units used for each measurement. What kinds of unitsare used for each? How can this help you remember the formula for thearea of a circle?
Reading to Learn MathematicsArea of Circles
NAME ________________________________________ DATE ______________ PERIOD _____
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Seki KowaJapanese mathematician Seki Kowa (c. 1642–1708) is called The Arithmetical Sage because of his many contributions to the development of mathematics in Japan. Before Seki, mathematics in Japan was considered a form of art to be enjoyed by intellectuals in their leisure time. Seki demonstrated the practical uses of mathematics and introduced social reforms that made it possible for anyone, not just intellectuals, to study mathematics.
One of Seki’s contributions to mathematics was his calculation of a valueof � that was correct to eighteen decimal places.
� � 3.141592653589793238…
Seki had noticed the phenomenon that you see at the right: as thenumber of sides of a regular polygon increases, the polygon looksmore and more like a circle. So, Seki calculated the following ratiofor polygons of increasingly many sides.
As the number of sides of the polygon gets larger, this ratio must getcloser to the ratio of the circumference of the circle to the diameter ofthe circle. This ratio, of course, is �.
You are given information below about a regular polygon and thecircle drawn around the polygon. Use a calculator to find Seki’sratio. (Give as many decimal places as there are in your calculator display.) What do you notice about your answers?
1. length of one side � 5 2. length of one side � 4.5922number of sides � 6 number of sides � 8diameter of circle � 10 diameter of circle � 12
3. length of one side � 3.7544 4. length of one side � 37.5443number of sides � 20 number of sides � 20diameter of circle � 24 diameter of circle � 240
5. length of one side � 1.6754 6. length of one side � 2.6389number of sides � 150 number of sides � 500diameter of circle � 80 diameter of circle � 420
perimeter of regular polygon������diameter of circle drawn around the polygon
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
© Glencoe/McGraw-Hill 638 Mathematics: Applications and Concepts, Course 2
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© Glencoe/McGraw-Hill 639 Mathematics: Applications and Concepts, Course 2
Study Guide and InterventionArea of Complex Figures
Find the area of the figure at the rightin square feet.
The figure can be separated into a rectangle and a trapezoid. Find the area of each.
Area of Rectangle
A � �w Area of a rectangle
A � 12 � 8 Replace � with 12 and w with 8.
A � 96 Multiply.
Area of Trapezoid
A � �12�h(b1 � b2) Area of a trapezoid
A � �12�(4)(4 � 12) Replace h with 4, b1 with 4, and b2 with 12.
A � 32 Multiply.
The area of the figure is 96 � 32 or 128 square feet.
Find the area of each figure. Round to the nearest tenth if necessary.
1. 2.
3. 18 mm
38 mm
11 mm
4 in. 5 in.
4 cm
6.5 cm
13 cm
6 cm
6 cm
12 ft
4 ft
4 ft
12 ft
8 ft
12 ft
4 ft
4 ft
8 ft
NAME ________________________________________ DATE ______________ PERIOD _____
Complex figures are made of circles, rectangles, squares, and other two-dimensional figures. To findthe area of a complex figure, separate it into figures whose areas you know how to find, and then addthe areas.
© Glencoe/McGraw-Hill 640 Mathematics: Applications and Concepts, Course 2
Practice: SkillsArea of Complex Figures
Find the area of each figure. Round to the nearest tenth if necessary.
1. 2.
3. 4.
5. 6.
7. 8.1.3 ft
1.3 ft
3.5 ft
3.5 ft
3.5 ft
3.5 ft4 m
4 m
2 m
2 m
2 m
20 yd
9 yd11 yd
9 yd
4 yd 4 yd
13 m
9 m
7 m
3 in. 4 in.
9 in.15 in.
5 in.
10 in.
30 in.
15 in.
7 mm5 mm
6 mm
7 cm
7 cm
NAME ________________________________________ DATE ______________ PERIOD _____
© Glencoe/McGraw-Hill 641 Mathematics: Applications and Concepts, Course 2
Practice: Word ProblemsArea of Complex Figures
ARCHITECTURE For Exercises 1–6 use Jaco’spreliminary design of his vacation house at the right. Round to the nearest tenth ifnecessary.
8 ft4 ft
4 ft
4 ft
8 ft 4 ft
4 ft
4 ft
8 ft
8 ft 4 ft4 ft
2 ft
4 ft12 ft 4 ft
12 ft
16 ft
16 ft12 ft
16 ft
16 ft
4 ft 4 ft
bedroom1
kitchen bedroom2
bathroom
livingroomden
NAME ________________________________________ DATE ______________ PERIOD _____
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1. What type of figure is bedroom 1? Findthe area of bedroom 1.
2. What is the area of the bedroom 2?What figures did you use to find thearea?
3. What is the area of the bathroom?What are the dimensions of the figuresyou used to find this area?
4. What is the area of the living room?How many figures did you use to findthis area?
5. What is the area of the den? Whatwould the area of the den be if thesemicircular window were removed andreplaced with a flat window?
6. What is the area of the kitchen? If Jacoadds a rectangular cooking island inthe middle of the kitchen withdimensions 6 feet by 4 feet, how manysquare feet of walking space will beleft?
© Glencoe/McGraw-Hill 642 Mathematics: Applications and Concepts, Course 2
Reading to Learn MathematicsArea of Complex Figures
Pre-Activity Read the introduction at the top of page 498 in your textbook.Write your answers below.
1. Describe the shape of the kitchen.
2. How could you determine the area of the kitchen?
3. How could you determine the total square footage of a house with rooms shapedlike these?
Reading the Lesson4. Look up the term footage in a dictionary. Write the meaning that matches
the way the term is used in this lesson.
5. What do you think the term square footage means?
6. Which word of the compound square footage indicates area? Explain.
7. Look up the term two-dimensional in a dictionary.
8. Name two dimensions of each of the following figures.
a. rectangle b. parallelogram c. triangle
9. Refer to the figure in Example 2 on page 499. How do you know that the baseand height of the triangle are each 4 inches long?
Helping You Remember10. Look in a dictionary for the meanings of the word complex when used as
an adjective. Write the meaning of the word as it is used in this lesson.Why can the figures in Examples 1 and 2 be considered complex figures?
NAME ________________________________________ DATE ______________ PERIOD _____
© Glencoe/McGraw-Hill 643 Mathematics: Applications and Concepts, Course 2
Extending the Pythagorean TheoremThe Pythagorean Theorem says that the sum of the areas of thetwo smaller squares is equal to the area of the largest square.Show that the Pythagorean Theorem can be extended to includeother shapes on the sides of a triangle. To do so, find the areas ofthe two smaller shapes. Then, check that their sum equals thearea of the largest shape.
1. area of smallest shape: 2. area of smallest shape:
area of middle shape: area of middle shape:
area of largest shape: area of largest shape:
3. area of smallest shape: 4. area of smallest shape:
area of middle shape: area of middle shape:
area of largest shape: area of largest shape:
3 in.
3 in.
3 in.
5 in.
5 in.
5 in.
4 in.
4 in.4 in.
3 in.
3 in.
5 in.5 in.
4 in.
4 in.
1.5in.
3 in.
5 in.
4 in.
2.5 in.
2 in.
5 in.
4 in.
3 in.
55
44 3
3
EnrichmentNAME ________________________________________ DATE ______________ PERIOD _____
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© Glencoe/McGraw-Hill 644 Mathematics: Applications and Concepts, Course 2
Study Guide and InterventionArea Models and Probability
A randomly-dropped counter falls somewhere in the squares. Find the probability that it falls on the shaded squares.
probability �
�
Area of Shaded Squares Area of All Squares
A � �r2 Area of a circle A � �12�bh Area of a triangle
A � � � 12 r � 1 A � �12�(5)(6) b � 5 and h � 6
A � 3.1 Simplify. A � 15 Simplify.
So, the probability of a counter falling in the shaded squares is about �31.51� or
about 20.7%.
A randomly-dropped counter falls in the squares. Find theprobability that it falls in the shaded squares. Write as a percent.Round to the nearest tenth if necessary.
1. 2. 3.
4. 5. 6.
area of shaded squares���area of all squares
number of ways to land in shaded squares�����number of ways to land on squares
NAME ________________________________________ DATE ______________ PERIOD _____
You can relate probability to the area of geometric shapes.
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© Glencoe/McGraw-Hill 645 Mathematics: Applications and Concepts, Course 2
Practice: SkillsArea Models and Probability
A randomly-dropped counter falls in the squares. Find theprobability that it falls in the shaded squares. Write as a percent.Round to the nearest tenth if necessary.
1. 2.
3. 4.
5. 6.
7. 8.
NAME ________________________________________ DATE ______________ PERIOD _____
© Glencoe/McGraw-Hill 646 Mathematics: Applications and Concepts, Course 2
Practice: Word ProblemsArea Models and Probability
GAMES Each figure represents a square dartboard. If it is equallylikely that a thrown dart will land anywhere on the dartboard, findthe probability that it lands in the shaded region. Round to thenearest tenth.
NAME ________________________________________ DATE ______________ PERIOD _____
1. 2.
17.5%
3. 4.
9.6%
5 cm
30 cm
10 cm
2 in.
12 in.
2 in.
4 in.
8 in.
12 in.
4 in.11.3 in.
16 in.
© Glencoe/McGraw-Hill 647 Mathematics: Applications and Concepts, Course 2
Reading to Learn MathematicsArea Models and Probability
Pre-Activity Complete the Mini Lab at the top of page 501 in your textbook.Write your answers below.
1. Do certain products occur more often?
2. Make and complete the table below to find all the possible outcomes.
Reading the Lesson3. How can you use the grid following the introduction in your textbook to
determine that the probability of rolling two numbers whose product is 6or 12 is �
29�?
4. The formula for probability is �detostiraeldar
aeraea
�. How does this lesson simplify
the expression for probability?
Helping You Remember5. Find the dimensions of a target for darts or for a bow and arrow. Draw a
model that shows the measurements. Then show the probability of hittingthe area that scores the most points per hit.
NAME ________________________________________ DATE ______________ PERIOD _____
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� 1 2 3 4 5 6
1 1 2 3
2 2 4 6
3
4
5
6
Area Formulas for Regular PolygonsRecall that the sides of a regular polygon are all the same length. Here aresome area formulas for four of the regular polygons. The variable s standsfor the length of one side.
triangle pentagon hexagon octagon
A � �s42� �3� A � �
s42� �25 � 1�0�5�� A � �
32s2� �3� A � 2s2(�2� � 1)
Find the area of each polygon with the side of given length. Use acalculator and round each answer to the nearest tenth.
1.
2.
3.
4.
Now use the table above to find the area of each shaded region below.Unless otherwise specified, each segment is 1 centimeter long.
5. 6. 7.
8. 9. 10.
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
© Glencoe/McGraw-Hill 648 Mathematics: Applications and Concepts, Course 2
Length ofa Side
Triangle Pentagon Hexagon Octagon
1 cm
2 cm
3 cm
4 cm
2 cm2 cm
3 cm
Write the letter for the correct answer in the blank at the right of each question.
1. Find 52.A. 10 B. 25 C. 52 D. 7 1.
2. Find 182.F. 36 G. 162 H. 18 I. 324 2.
3. Find �2,500�.A. 50 B. 500 C. 1,250 D. 250 3.
4. Estimate �37� to the nearest whole number.F. 18 G. 19 H. 7 I. 6 4.
5. Estimate �143� to the nearest whole number.A. 10 B. 11 C. 12 D. 20,499 5.
6. Estimate �899� to the nearest whole number.F. 20 G. 29 H. 30 I. 31 6.
7. Use a calculator to find �43� to the nearest tenth.A. 1,849 B. 6.6 C. 6.5 D. 3.5 7.
8. The lengths of the legs of a right triangle are 8 centimeters and6 centimeters. Which equation would you solve to find the length ofthe hypotenuse?F. 62 � x2 � 82 G. 82 � x2 � 62 H. 62 � 82 � x2 I. 82 � 62 � x2 8.
9. The length of the hypotenuse of a right triangle is 20 feet, and the lengthof one leg is 16 feet. Find the length of the other leg.A. 12 ft B. 72 ft C. 26 ft D. 36 ft 9.
10. Which could be the lengths of the sides of a right triangle?F. 6 m, 8 m, 9 m G. 11 ft, 12 ft, 14 ftH. 30 cm, 40 cm, 50 cm I. 3 cm, 4 cm, 7 cm 10.
11. ART A rectangular picture frame is 24 inches long by 18 inches wide. Adiagonal brace is nailed across the back of the frame from one corner tothe other. How long is the brace?A. 30 in. B. 42 in. C. 45 in. D. 21 in. 11.
12. What is the area of a parallelogram with a height of 4 yards and a baseof 5 yards?F. 80 yd2 G. 10 yd2 H. �
45� yd2 I. 20 yd2 12.
13. Find the area of a circle with a radius of 6 feet. Round to the nearest tenth.A. 113.1 ft2 B. 18.8 ft2 C. 452.4 ft2 D. 37.7 ft2 13.
Chapter 11 Test, Form 1
© Glencoe/McGraw-Hill 649 Mathematics: Applications and Concepts, Course 2
Ass
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NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Ass
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Find the area of each figure. Round to the nearest tenth if necessary.
14.F. 5,026.5 m2 G. 125.7 m2
H. 1,256.6 m2 I. 62.8 m2 14.
15.A. 47 m2 B. 75 m2
C. 60 m2 D. 165 m2 15.
16.F. 104.5 m2 G. 660 m2
H. 330 m2 I. 225.5 m2 16.
17.A. 15 in2 B. 50 in2
C. 2 in2 D. 500 in2 17.
18.F. 56 m2 G. 144 m2
H. 2,560 m2 I. 104 m2 18.
A randomly-dropped counter falls in the squares. Find the probability that it falls in the shaded squares. Write as a percent. Round to the nearest tenth if necessary.
19.A. 21.7% B. 16.7%C. 12.2% D. 5.0% 19.
20.F. 8.3% G. 50%H. 25% I. 20% 20.
Bonus Find ��121�. B:
8 m
8 m
10 m
10 in.
5 in.
41 m
19 m
11 m
8 m
15 m
10 m
40 m
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 11 Test, Form 1 (continued)
© Glencoe/McGraw-Hill 650 Mathematics: Applications and Concepts, Course 2
Write the letter for the correct answer in the blank at the right of each question.
1. Find 102.A. 12 B. 20 C. 1,000 D. 100 1.
2. Find 422.F. 1,008 G. 420 H. 1,764 I. 84 2.
3. Find �841�.A. 29 B. 210 C. 52 D. 31 3.
4. Estimate �90� to the nearest whole number.F. 10 G. 8 H. 9 I. 11 4.
5. Estimate �178� to the nearest whole number.A. 14 B. 13 C. 12 D. 19 5.
6. Estimate �1,001� to the nearest whole number.F. 31 G. 32 H. 33 I. 20 6.
7. Use a calculator to find �267� to the nearest tenth.A. 17.4 B. 16.7 C. 71,289 D. 16.3 7.
8. The lengths of the legs of a right triangle are 22 feet and 19 feet. Whichequation would you solve to find the length of the hypotenuse?F. 222 � x2 � 192 G. 192 � 222 � x2
H. 192 � x2 � 222 I. 192 � 222 � x2 8.
9. The length of one leg of a right triangle is 21 inches and the length ofthe hypotenuse is 35 inches. Find the length of the other leg.A. 12 in. B. 1,268.5 in. C. 28 in. D. 14 in. 9.
10. Which could be the lengths of the sides of a right triangle?F. 18 m, 24 m, 30 m G. 2 cm, 3 cm, 4 cmH. 19 ft, 27 ft, 39 ft I. 56 in., 112 in., 168 in. 10.
11. TELEVISION A 41-foot guy wire is used to brace an antenna. The wire isanchored 9 feet from the base of the antenna. How tall is the antenna?A. 42 ft B. 40 ft C. 80 ft D. 22 ft 11.
12. What is the area of a parallelogram with a base of 6 inches and a heightof 8 inches?F. 96 in2 G. �
34� in2 H. 24 in2 I. 48 in2 12.
13. Find the area of a circle with a diameter of 24 feet. Round to the nearesttenth.A. 1,809.6 ft2 B. 37.7 ft2 C. 452.4 ft2 D. 75.4 ft2 13.
Chapter 11 Test, Form 2A
© Glencoe/McGraw-Hill 651 Mathematics: Applications and Concepts, Course 2
Ass
essm
ent
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Find the area of each figure. Round to the nearest tenth if necessary.
14.F. 254.5 mm2 G. 28.3 mm2
H. 1,017.9 mm2 I. 56.5 mm2 14.
15.A. 225 m2 B. 360 m2
C. 180 m2 D. 450 m2 15.
16.F. 60 cm2 G. 96 cm2
H. 120 cm2 I. 48 cm2 16.
17.A. 72 m2 B. 108 m2
C. 54 m2 D. 36 m2 17.
18.F. 116.5 in2 G. 50.1 in2
H. 74.1 in2 I. 85.1 in2 18.
A randomly-dropped counter falls in the squares. Find the probability that it falls in the shaded squares. Write as a percent. Round to the nearest tenth if necessary.
19.A. 0.1% B. 13.3%C. 80.0% D. 15.5% 19.
20.
F. 26.7% G. 16%H. 0.3% I. 33.3% 20.
Bonus Find ��529�. B:
6 in.
8 in.
4 in.
6 m
12 m
9 m
15 cm
9 cm
5 cm 4 cm
12 m15 m
30 m
9 mm
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 11 Test, Form 2A (continued)
© Glencoe/McGraw-Hill 652 Mathematics: Applications and Concepts, Course 2
Write the letter for the correct answer in the blank at the right of each question.
1. Find 112.A. 22 B. 121 C. 13 D. 110 1.
2. Find 302.F. 450 G. 60 H. 300 I. 900 2.
3. Find �196�.A. 14 B. 98 C. 49 D. 16 3.
4. Estimate �23� to the nearest whole number.F. 4 G. 11 H. 6 I. 5 4.
5. Estimate �102� to the nearest whole number.A. 10 B. 11 C. 12 D. 25 5.
6. Estimate �520� to the nearest whole number.F. 20 G. 22 H. 23 I. 24 6.
7. Use a calculator to find �173� to the nearest tenth.A. 29,929 B. 13.2 C. 5.6 D. 13.1 7.
8. The lengths of the legs of a right triangle are 16 feet and 30 feet. Whichequation would you solve to find the length of the hypotenuse?F. 162 � x2 � 30 G. 162 � 302 � x2
H. 302 � x2 � 16 I. 302 � 162 � x2 8.
9. The length of one leg of a right triangle is 24 meters, and the length ofthe hypotenuse is 25 meters. Find the length of the other leg.A. 7 m B. 35 m C. 49 m D. 1 m 9.
10. Which could be the lengths of the sides of a right triangle?F. 7 cm, 8 cm, 10 cm G. 20 m, 30 m, 40 mH. 12 ft, 15 ft, 20 ft I. 6 cm, 8 cm, 10 cm 10.
11. TRAVEL The Garcias drove 24 miles east and then 7 miles north. Atthat point, what is the straight-line distance from their starting point?A. 31 mi B. 625 mi C. 312.5 mi D. 25 mi 11.
12. What is the area of a parallelogram with a base of 4 miles and a heightof 8 miles?F. �
12� mi2 G. 32 mi2 H. 16 mi2 I. 64 mi2 12.
13. Find the area of a circle with a radius of 20 yards. Round to the nearest tenth.A. 62.8 yd2 B. 31.4 yd2 C. 314.2 yd2 D. 1,256.6 yd2 13.
Chapter 11 Test, Form 2B
© Glencoe/McGraw-Hill 653 Mathematics: Applications and Concepts, Course 2
Ass
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ent
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Find the area of each figure. Round to the nearest tenth if necessary.
14.F. 10,207.0 m2 G. 179.1 m2
H. 89.5 m2 I. 2,551.8 m2 14.
15.A. 374 cm2 B. 289 cm2
C. 578 cm2 D. 187 cm2 15.
16.F. 735 mm2 G. 367.5 mm2
H. 588 mm2 I. 294 mm2 16.
17.A. 56 m2 B. 40 m2
C. 28 m2 D. 20 m2 17.
18.F. 89.1 mi2 G. 164.5 mi2
H. 105.1 mi2 I. 81.1 mi2 18.
A randomly-dropped counter falls in the squares. Find the probability that it falls in the shaded squares. Write as a percent. Round to the nearest tenth if necessary.
19.A. 3.8% B. 26.3%C. 26.4% D. 0.3% 19.
20.F. 12% G. 40%H. 5% I. 20% 20.
Bonus Find ��729�. B:
6 cm4 cm
12 cm
8 cm
5 m
8 m
7 m
29 mm
20 mm
15 mm 12 mm
11 cm17 cm
34 cm
57 m
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 11 Test, Form 2B (continued)
© Glencoe/McGraw-Hill 654 Mathematics: Applications and Concepts, Course 2
Chapter 11 Test, Form 2C
© Glencoe/McGraw-Hill 655 Mathematics: Applications and Concepts, Course 2
Ass
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ent
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
1. A randomly-dropped counter falls in the squares. Find the 1.probability that it falls in the shaded squares. Write as a percent. Round to the nearest tenth if necessary.
2. CONSTRUCTION A 15-foot ladder is propped against a wall. 2.The base of the ladder is 9 feet from the base of the wall.How far up the wall does the ladder reach?
3. Evaluate a2 � �b� if a � 4 and b � 9. 3.
Find the square of each number.
4. 9 4.
5. 40 5.
Find each square root.
6. �144� 6.
7. �1,369� 7.
Estimate each square root to the nearest whole number.
8. �29� 8.
9. �53� 9.
Use a calculator to find each square root to the nearesttenth.
10. �90� 10.
11. �455� 11.
Find the missing measure of each right triangle. Roundto the nearest tenth if necessary.
12. b � 7 cm, c � 11 cm 12.
Chapter 11 Test, Form 2C (continued)
13. a � 30 ft, c � 50 ft 13.
14. 14.
Find the area of each figure. Round to the nearest tenth if necessary.
15. 15.
16. 16.
17. 17.
18. 18.
Find the area of each circle. Round to the nearest tenth.
19. radius � 6 cm 19.
20. 20.
Bonus What is the base of a parallelogram if the height is B:17.5 inches and the area is 245 square inches?
34 in.
16 mi
25 mi
11 mi
15 m
20 m
8 mm14 mm
27 mm
7 ft
8 ft
4 ft
4.3 m
2 m
c m
NAME ________________________________________ DATE ______________ PERIOD _____
© Glencoe/McGraw-Hill 656 Mathematics: Applications and Concepts, Course 2
Chapter 11 Test, Form 2D
1. A randomly-dropped counter falls in the squares. Find the 1.probability that it falls in the shaded squares. Write as a percent. Round to the nearest tenth if necessary.
2. TRAVEL Sally drives 10 miles east and then 10 miles south. 2.At this point, what is the straight-line distance from her starting point? Estimate to the nearest whole number.
3. Evaluate a2 � �b� if a � 9 and b � 4. 3.
Find the square of each number.
4. 4 4.
5. 30 5.
Find each square root.
6. �121� 6.
7. �1,089� 7.
Estimate each square root to the nearest whole number.
8. �39� 8.
9. �84� 9.
Use a calculator to find each square root to the nearest tenth.
10. �80� 10.
11. �320� 11.
Find the missing measure of each right triangle. Roundto the nearest tenth if necessary.
12. a � 45 m, b � 60 m 12.
13. a � 5 ft, c � 8 ft 13.
© Glencoe/McGraw-Hill 657 Mathematics: Applications and Concepts, Course 2
Ass
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ent
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
14. 14.
Find the area of each figure. Round to the nearest tenthif necessary.
15. 15.
16. 16.
17. 17.
18. 18.
Find the area of each circle. Round to the nearest tenth.
19. diameter � 7 ft 19.
20. 20.
Bonus What is the base of a parallelogram if the height is B:14.5 feet and the area is 174 square feet?
14 in.
42 cm
22 cm
18 cm
4 in.
8 in.
50 mm
25 mm20 mm
6 m4 m
9 m
6.3 cm
x cm
10 cm
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 11 Test, Form 2D (continued)
© Glencoe/McGraw-Hill 658 Mathematics: Applications and Concepts, Course 2
Chapter 11 Test, Form 3
1. A randomly-dropped counter falls 1.in the squares. Find the probabilitythat it falls in the shaded squares.Write as a percent. Round to thenearest tenth if necessary.
2. BOATING A 25-foot cable is used to brace 2.a ship mast. The cable is anchored 7 feetfrom the foot of the mast. How tall is the mast?
3. Evaluate a2 � �b� if a � 16 and b � 9. 3.
Find the square of each number.
4. 19 4.
5. 32 5.
Find each square root.
6. �441� 6.
7. �256� 7.
Estimate each square root to the nearest whole number.
8. �84� 8.
9. �141� 9.
Use a calculator to find each square root to the nearest tenth.
10. �68� 10.
11. �932� 11.
Find the missing measure of each right triangle. Round to the nearest tenth if necessary.
12. b � 64 m, c � 80 m 12.
13. a � 11 yd, c � 18 yd 13.
14. 14.
8.7 in.c in.
5 in.
© Glencoe/McGraw-Hill 659 Mathematics: Applications and Concepts, Course 2
Ass
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NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Chapter 1 Test, Form 3 (continued)
Find the area of each figure. Round to the nearest tenth if necessary.
15. 15.
16. 16.
17. 17.
18. 18.
Find the area of each circle. Round to the nearest tenth.
19. diameter � 100 ft 19.
20. 20.
Bonus What is the height of a parallelogram if the base is B:22 inches and the area is 407 square inches?
19.3 m
57 cm
20 cm
33 cm
6 ft
8 ft
10 ft5 ft
24 m
30 m
25 m
16 cm
10 cm
NAME ________________________________________ DATE ______________ PERIOD _____
© Glencoe/McGraw-Hill 660 Mathematics: Applications and Concepts, Course 2
Demonstrate your knowledge by giving a clear, concise solution toeach problem. Be sure to include all relevant drawings and justifyyour answers. You may show your solutions in more than one wayor investigate beyond the requirements of the problem. If necessary,record your answer on another piece of paper.
1. a. Explain in your own words what is meant by the square root of anumber.
b. Use a model to show that �17� is about 4.
c. State the Pythagorean Theorem in your own words.
d. Use a right triangle and squares to model 62 � 82 � 102.
e. CARPENTRY A carpenter is framing a house. The front of the house measures 48 feet. The width measures 36 feet. He measures diagonally across the house as shown. If the diagonal measurement is 62 feet, are the corners of the house square (right angles)? Explain your reasoning. Use a calculator.
f. CARPENTRY The carpenter is cutting a brace to keep a window frame square during installation.What is the length of the brace? Explain eachstep. Use a calculator. Round to the nearest tenthif necessary.
2. LANDSCAPING Mrs. Cobel is preparing a bid for sodding a new city park. Her bid is for sodding all of the park except the fountain and garden areas. If she plans to submit a bid for $1.50 per square foot, tell what Mrs. Cobel’s bid will be. Show your work and explain your reasoning. Round to the nearest dollar.
145 ft
300 ft
350 ft
175
ft12
5 ft
fountaingarden
20 ft
30 in.
36 in.
brace
48 ft
36 ft62 ft
Chapter 11 Extended Response Assessment
© Glencoe/McGraw-Hill 661 Mathematics: Applications and Concepts, Course 2
Ass
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NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Write whether each sentence is true or false. If false, replacethe underlined term to make a true sentence.
1. To double a number means to multiply that number by itself. 1.
2. An irrational number is a number that cannot be written as 2.a fraction.
3. The diagonal of a rectangle is the leg of a right triangle. 3.
4. A leg is one of the two sides adjacent to the right side of a 4.right triangle.
5. The leg is the side of a right triangle that is opposite the 5.right angle.
6. The height of a parallelogram is the perpendicular distance 6.from the base to the opposite side.
7. A plus sign is the symbol used to indicate the positive square 7.root of a number.
8. A perfect square is the square of a rational number. 8.
9. Two-dimensional figures made up of more than one type of 9.figure are called three-dimensional figures.
10. Square roots are the factors multiplied to form perfect 10.squares.
In your own words, define the term.
11. Pythagorean Theorem
base (p. 483)
complex figure (p. 498)
height (p. 483)
hypotenuse (p. 479)
irrational number (p. 476)
leg (p. 479)
perfect square (p. 471)
Pythagorean Theorem (p. 479)
radical sign (p. 471)
square (p. 470)
square roots (p. 471)
Chapter 11 Vocabulary Test/Review
© Glencoe/McGraw-Hill 662 Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Ass
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ent
© Glencoe/McGraw-Hill 663 Mathematics: Applications and Concepts, Course 2
Find the square of each number. 1.
1. 23 2. 43 3. 36 2.
3.
Find each square root. 4.
4. �36� 5. �361� 6. �676� 5.
6.
Estimate each square root to the nearest whole number. 7.
7. �63� 8. �150� 8.
9. �223� 10. �292� 9.
10.
Find the missing measure of each right triangle. Round to the nearest tenth if necessary.
1. 2. 1.
2.
3. a � 28 mm, c � 35 mm 3.
Find the area of each parallelogram. Round to the nearest tenth if necessary.
4. 5. 4.
5.
39 ft
24 ft17 ft
8.9 m
4.3 m
9 cm12 cm
a cm
48 ft
14 ftc ft
Chapter 11 Quiz(Lessons 11-1 and 11-2)
Chapter 11 Quiz(Lessons 11-3 and 11-4)
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
© Glencoe/McGraw-Hill 664 Mathematics: Applications and Concepts, Course 2
Find the area of each figure. 1.
1. 2. 3. 2.
3.
Find the area of each circle. Round to the nearest tenth. 4.
4. radius � 4 in. 5. 5.
3.6 cm
30 ft
20 ft
68 ft
18 ft
65 mm
60 mm80 mm64 m
80 m
120 m
Find the area of each figure. Round to the nearest tenth if necessary.
1. 2. 1.
2.
A randomly-dropped counter falls in the squares. Find the probability that it falls in the shaded squares. Write as a percent. Round to the nearest tenth if necessary.
3. 4. 5. 3.
4.
5.
3 in.
4 in.
5 in.5 ft
9 ft
Chapter 11 Quiz(Lessons 11-5 and 11-6)
Chapter 11 Quiz(Lessons 11-7 and 11-8)
Write the letter for the correct answer in the blank at the right of each question.
1. Find 92.A. 18 B. 3 C. 81 D. 11 1.
2. Find �144�.F. 12 G. 13 H. 20,736 I. 72 2.
3. Estimate �60� to the nearest whole number.A. 3,600 B. 30 C. 7 D. 8 3.
4. Use a calculator to find �87� to the nearest tenth.F. 9.3 G. 9 H. 43.5 I. 7,569.0 4.
5. Find the missing measure for the triangle.A. 625 m B. 25 mC. 5 m D. 6 m 5.
6. Find the area of the parallelogram.F. 36 in2 G. 18 in2
H. 72 in2 I. 70 in2 6.
Find the square of each number. 7.
7. 9 8. 16 8.
Find each square root. 9.
9. �225� 10. �324� 10.
Estimate each square root to the nearest whole number. 11.
11. �290� 12. �407� 12.
Find the missing measure of each right triangle. Roundto the nearest tenth if necessary. 13.
13. a � 12 cm; c � 13 cm 14. a � 11 m; c � 23 m 14.
15. SKATEBOARDING 15.A skateboarding ramp is4.5 meters long and 2.75 meters tall. To the nearesttenth, how long across the ground is the ramp?
2.75 m4.5 m
12 in.
6 in.
20 m
15 mc m
Chapter 11 Mid-Chapter Test(Lessons 11–1 through 11-4)
© Glencoe/McGraw-Hill 665 Mathematics: Applications and Concepts, Course 2
Ass
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NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
1. Simplify 6(�3e). (Lesson 3-6) 1.
2. Write �1350�
in simplest form. (Lesson 5-3) 2.
3. Find 5�58� � 5�
15�. Write in simplest form. (Lesson 6-4) 3.
4. Solve the proportion �n5
� � �3258�
. (Lesson 7-3) 4.
5. Write 13.8% as a fraction in simplest form. (Lesson 7-5) 5.
6. 30 is what percent of 12? (Lesson 8-2) 6.
7. The forecast for Saturday calls for a 45% chance of snow. 7.Describe the complementary event and its probability.(Lesson 9-1)
8. Determine whether a regular decagon can be used by itself 8.to make a tessellation. Explain. (Lesson 10-7)
9. Triangle PQR have vertices P(1, 2), Q(3, 5), and R(6, 0). Find 9.the vertices of P�Q�R� after a translation of 3 units left and 2 units down. Then graph. (Lesson 10-8)
10. Estimate �120� to the nearest whole number. (Lesson 11-2) 10.
11. STUNTS A monster truck attempted to scale a brick wall. 11.The highest point it reached on the wall was 3 meters. At that point, its rear wheels were 4.3 meters from the wall.How long is the monster truck? Round to the nearest hundredth. (Lesson 11-3)
12. Find the area of a triangle with a base measure of 12.10.5 millimeters and a height of 6 millimeters. (Lesson 11-5)
13. Find the area of the circle. Round to the 13.nearest tenth. (Lesson 11-6) 1.5 in.
y
xO
P
Q
R
Chapter 11 Cumulative Review(Chapters 1–11)
© Glencoe/McGraw-Hill 666 Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Ass
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ent
© Glencoe/McGraw-Hill 667 Mathematics: Applications and Concepts, Course 2
1. Evaluate |�8| � |�2|. (Lesson 3-1)
A. �6 B. 10 C. 6 D. �10 1.
2. Write 49.5% as a decimal. (Lesson 5-6)
F. 0.495 G. 4.95 H. 0.0495 I. 4.095 2.
3. Write 0.33% as a decimal. (Lesson 7-6)
A. 0.0033 B. 33 C. 3.3 D. 0.033 3.
4. Find the percent of change from 18 to 41. Round to the nearestwhole percent. (Lesson 8-4)
F. 44% G. 228% H. 56% I. 128% 4.
5. RAFFLE In a raffle, one ticket will be drawn from a total of 200 tickets. If Maureen has 4 tickets, what is the probability that she will win? (Lesson 9-1)
A. �510�
B. �14� C. 0.2 D. 4% 5.
6. HORSES Tionna has a display that holds 8 horse figurines.If she has 17 horse figurines, how many combinations of 8 can she create? (Lesson 9-5)
F. 40,320 G. 136 H. 2,312 I. 24,310 6.
7. Suppose �1 and �2 are complementary. If m�1 � 50º, findm�2. (Lesson 10-3)
A. 30º B. 50º C. 40º D. 130º 7.
8. Three sides of a triangle measure 6 meters, 4 meters, and5 meters. Classify the triangle by its sides. (Lesson 10-4)
F. scalene G. isosceles H. equilateral I. obtuse 8.
9. CABLE A 52-foot cable reaches from the top of a pole to a point on the ground that is 48 feetfrom the base of the pole. How tall is the pole?(Lesson 11-3)
A. 12 ft B. 20 ftC. 92 ft D. 50 ft 9.
10. What is the base of a parallelogram with an area of 30 squaremiles and a height of 5 miles? (Lesson 11-4)
F. 35 mi G. 25 mi H. 152 mi I. 6 mi 10.
11. Find the area of a circle with a diameter of 36 millimeters.Round to the nearest tenth. (Lesson 11-6)
A. 4071.5 mm2 B. 56.5 mm2
C. 113.1 mm2 D. 1017.9 mm2 11. DCBA
IHGF
DCBA
52 ft
48 ft
IHGF
DCBA
IHGF
DCBA
IHGF
DCBA
IHGF
DCBA
Standardized Test Practice(Chapters 1–11)
Part 1: Multiple Choice
Instructions: Fill in the appropriate oval for the best answer.
12. Order 11, �14, �8, �10, 0, and �3 from least to greatest. 12.(Lesson 3-2)
13. A rectangle has a width of 3.5 inches and 13. 14.a length of 4.25 inches. Find the perimeter of the rectangle in inches. (Lesson 6-8)
14. BAND The ratio of boys to girls in the school band is 2 to 3. If there are 90 students in the band, how many of them are boys?(Lesson 7-3)
15. Use the Fundamental Counting Principle 15.to find the total number of outcomes when choosing a day in the month of September and tossing two coins. (Lesson 9-3) 16.
16. ATHLETICS A rectangular athletic field is 80 meters long by 60 meters wide. What is the diagonal distance across the field in meters? (Lesson 11-3)
17. WINDSTORM A strong storm blew over a billboard 27 feet tall so that it is leaning against a telephone pole 21 feet tall. (Lesson 11-3)
a. Make a drawing to represent this situation.
b. How far from the base of the telephone pole is the base of thebillboard? Round to the nearest tenth if necessary.
Part 3: Extended Response
Instructions: Write your answers below or to the right of the questions.
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
Part 2: Short Response/Grid In
Instructions: Enter your grid in answers by writing each digit of the answer in acolumn box and then shading in the appropriate circle that corresponds to that entry.Write answers to short answer questions in the space provided.
NAME ________________________________________ DATE ______________ PERIOD _____
Standardized Test Practice (continued)
(Chapters 1–11)
© Glencoe/McGraw-Hill 668 Mathematics: Applications and Concepts, Course 2
An
swer
s
© Glencoe/McGraw-Hill A1 Mathematics: Applications and Concepts, Course 2
Standardized Test PracticeStudent Recording Sheet (Use with pages 508–509 of the Student Edition.)
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Part 1:
Solve the problem and write your answer in the blank.
For grid in questions, also enter your answer by writing each number or symbolin a box. Then fill in the corresponding circle for that number or symbol.
11. 19.
12.
13.
14.
15.
16.
17.
18.
19. (grid in)
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
Select the best answer from the choices given and fill in the corresponding oval.
Multiple Choice
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. IHGF
DCBA
IHGF
DCBA
IHGF
DCBA
IHGF
DCBA
IHGF
DCBA
Part 2: Short Response/Grid in
Record your answer for Question 20 on the back of this paper.
Part 3: Extended Response
General Scoring Guidelines• If a student gives only a correct numerical answer to a problem but does not show how he or she
arrived at the answer, the student will be awarded only 1 credit. All extended response questionsrequire the student to show work.
• A fully correct answer for a multiple-part question requires correct responses for all parts of thequestion. For example, if a question has three parts, the correct response to one or two parts of thequestion that required work to be shown is not considered a fully correct response.
• Students who use trial and error to solve a problem must show their method. Merely showing thatthe answer checks or is correct is not considered a complete response for full credit.
Exercise 20 Rubric
Standardized Test PracticeRubric (Use to score the Extended Response question on page 509 of the Student Edition.)
Score Specific Criteria4 The Pythagorean Theorem is used to determine the height of the parallelogram. An
accurate explanation that the area of the side (60 � 46.5 in2) is greater that the areaof the floor (60 � 30 in2) is given. The area of two triangular regions is correctlydetermined to be 1,320 in2.
3 The correct values are found. However, the explanation is correct but not complete.ORThe explanation is correct and complete, but one computational error is made infinding the height of the parallelogram or the area of the two triangular regions.
2 The Pythagorean Theorem is used to determine the height of the parallelogram, andthe explanation is correct and complete. However, the area of only one triangularregion is found. ORThe Pythagorean Theorem is used to determine the height of the parallelogram, thearea of the side is stated to be greater than the area of the floor, and the area of thetwo triangular regions is correctly determined. However, the explanation is incorrector not given.
1 The area of the two triangular regions is correct, but the answer to Part a iscompletely incorrect. ORThe area of the side is stated to be greater than the area of the floor, but theexplanation is incorrect or not given. The area of the two triangular regions isincorrect.
0 Response is completely incorrect.
© Glencoe/McGraw-Hill A2 Mathematics: Applications and Concepts, Course 2
© Glencoe/McGraw-Hill A3 Mathematics: Applications and Concepts, Course 2
An
swer
s
Fin
d t
he
squ
are
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NA
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____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice:
Ski
llsS
qu
ares
an
d S
qu
are
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athe
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6.
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7 �
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o �
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3.
A s
qu
are
tile
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an
are
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144
sq
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ches
.Wh
at a
re t
he
dim
ensi
ons
of t
he
tile
?
144
12F
ind
the
squa
re r
oot
of 1
44.
So,
the
tile
mea
sure
s 12
in
ches
by
12 i
nch
es.
Fin
d t
he
squ
are
of e
ach
nu
mb
er.
1.2
42.
981
3.14
196
4.15
225
5.21
441
6.45
2,02
5
Fin
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sq
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8.�
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____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Sq
uar
es a
nd
Sq
uar
e R
oo
ts
The
pro
duct
of
a nu
mbe
r an
d its
elf
is t
he s
qu
are
of t
he n
umbe
r.N
umbe
rs li
ke 4
, 25
, an
d 2.
25 a
reca
lled
per
fect
sq
uar
esbe
caus
e th
ey a
re s
quar
es o
f ra
tiona
l num
bers
.The
fact
ors
mul
tiplie
d to
form
perf
ect
squa
res
are
calle
d sq
uar
e ro
ots
.Bot
h 5
�5
and
(�5)
(�5)
equ
al 2
5.S
o, 2
5 ha
s tw
o sq
uare
root
s, 5
and
�5.
A r
adic
al s
ign
, �
00 �,
is t
he s
ymbo
l use
d to
indi
cate
the
pos
itive
squa
re r
oot
of a
num
ber.
So,
�25�
�5.
Answers (Lesson 11-1)
© Glencoe/McGraw-Hill A4 Mathematics: Applications and Concepts, Course 2
©G
lenc
oe/M
cGra
w-H
ill61
2M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Pre-
Act
ivit
yC
om
ple
te t
he
Min
i Lab
at
the
top
of
pag
e 47
0 in
yo
ur
text
bo
ok.
Wri
te y
ou
r an
swer
s b
elo
w.
1.O
n g
rid
pape
r,dr
aw a
nd
labe
l th
ree
oth
er
rect
angl
es t
hat
hav
e a
peri
met
er o
f 16
un
its.
2.S
um
mar
ize
the
dim
ensi
ons
and
area
s of
th
e re
ctan
gles
th
at
you
dre
w i
n a
tab
le l
ike
the
one
show
n b
elow
.
3.D
raw
th
ree
diff
eren
t re
ctan
gles
th
at h
ave
a pe
rim
eter
of
12 u
nit
s an
d fi
nd
thei
r ar
eas.
4.W
hat
do
you
not
ice
abou
t th
e re
ctan
gles
wit
h t
he
grea
test
are
as?
Th
ey a
re s
qu
ares
.
Rea
din
g t
he
Less
on
5a
–c.S
amp
le a
nsw
ers
are
giv
en.
5.In
th
is l
esso
n,t
he
wor
d sq
uar
eis
use
d in
sev
eral
dif
fere
nt
way
s.T
ell
the
mea
nin
g of
th
e w
ord
as i
t is
use
d in
eac
h p
hra
se o
r se
nte
nce
.a.
Fin
d th
e sq
uar
eof
3.
3 ti
mes
3b
.9 u
nit
s sq
uar
ed9
squ
are
un
its;
9 sq
uar
es w
ith
sid
es o
f 1
un
it e
ach
c.A
box
ing
rin
g is
a s
quar
ew
ith
an
are
a of
400
ft2
.a
rect
ang
le w
ith
eq
ual
sid
es
Hel
pin
g Y
ou
Rem
emb
er6.
Wor
k w
ith
a p
artn
er.U
se a
cal
cula
tor
to f
ind
the
squ
ares
of
six
nu
mbe
rs,
som
e of
th
em d
ecim
als.
Th
en w
rite
on
ly t
he
squ
ares
in
a l
ist
and
exch
ange
lis
ts w
ith
you
r pa
rtn
er.F
ind
the
squ
are
root
s of
th
e sq
uar
es i
nth
e li
st t
hat
you
rec
eive
.Wri
te y
our
answ
ers
in t
he
form
�x �
�y.
See
stu
den
ts’w
ork
.
5 un
its1
unit
4 un
its2
units
3 un
its
3 un
its
5 sq
uare
uni
ts8
squa
re u
nits
9 sq
uare
uni
ts
2 �
612 16
3 �
5
4 �
4
15
1 �
77
Dra
win
gD
imen
sio
ns
(un
its)
A
rea
(sq
un
its)
6 un
its
2 un
its
5 un
its
3 un
its
4 un
its
4 un
its
Read
ing
to L
earn
Mat
hem
atic
sS
qu
ares
an
d S
qu
are
Ro
ots
©G
lenc
oe/M
cGra
w-H
ill61
1M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice:
Wor
d Pr
oble
ms
Sq
uar
es a
nd
Sq
uar
e R
oo
ts
Lesson 11–1
1.FE
RTI
LIZE
RJo
hn
bou
ght
a ba
g of
law
nfe
rtil
izer
th
at w
ill
cove
r 40
0 sq
uar
efe
et.W
hat
are
th
e di
men
sion
s of
th
ela
rges
t sq
uar
e pl
ot o
f la
wn
th
at t
he
bag
of f
erti
lize
r w
ill
cove
r?20
ft
by 2
0 ft
2.G
EOM
ETRY
Th
e ar
ea A
of
a ci
rcle
in
squ
are
feet
wit
h a
rad
ius
r in
fee
t is
give
n a
ppro
xim
atel
y by
th
e fo
rmu
laA
�3.
14r2
.Wh
at i
s th
e ap
prox
imat
ear
ea o
f a
circ
le w
ith
a r
adiu
s of
3 f
eet?
28.2
6 ft
2
3.M
OTI
ON
Th
e ti
me
tin
sec
onds
for
an
obje
ct d
ropp
ed f
rom
a h
eigh
t of
hfe
etto
hit
th
e gr
oun
d is
giv
en b
y th
e
form
ula
t�
��2 3h 2� �.H
ow l
ong
wil
l it
tak
e
an o
bjec
t dr
oppe
d fr
om a
hei
ght
of
500
feet
to
hit
th
e gr
oun
d? R
oun
d to
the
nea
rest
ten
th.
5.6
s
4.PA
CK
AG
ING
A c
ardb
oard
en
velo
pe f
or a
com
pact
dis
c is
a s
quar
e w
ith
an
are
aof
171
.61
squ
are
cen
tim
eter
s.W
hat
are
the
dim
ensi
ons
of t
he
enve
lope
?13
.1 c
m b
y 13
.1 c
m
5.G
EOG
RA
PHY
Ref
er t
o th
e sq
uar
esbe
low
.Th
ey r
epre
sen
t th
e ap
prox
imat
ear
eas
of C
alif
orn
ia,A
laba
ma,
and
Neb
rask
a.F
ind
the
area
of A
laba
ma.
50,6
25 m
i2
277
mi
225
mi
395
mi
ALNE
CA
6.U
se t
he
figu
re i
n E
xerc
ise
5.H
ow m
uch
larg
er i
s C
alif
orn
ia t
han
Neb
rask
a?79
,296
mi2
Answers (Lesson 11-1)
© Glencoe/McGraw-Hill A5 Mathematics: Applications and Concepts, Course 2
An
swer
s
©G
lenc
oe/M
cGra
w-H
ill61
4M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Est
imat
e �
40�to
th
e n
eare
st w
hol
e n
um
ber
.
Lis
t so
me
perf
ect
squ
ares
.
1,4,
9,16
,25,
36,4
9,…
36�
40
�49
40 is
bet
wee
n th
e pe
rfec
t sq
uare
s 36
and
49.
�36�
��
40��
�49�
Fin
d th
e sq
uare
roo
t of
eac
h nu
mbe
r.
6�
�40�
�7
�36�
�6
and
�49�
�7
So,
�40�
is b
etw
een
6 a
nd
7.S
ince
40
is c
lose
r to
36
than
to
49,t
he
best
wh
ole
nu
mbe
res
tim
ate
is 6
.
Use
a c
alcu
lato
r to
fin
d t
he
valu
e of
�28 �
toth
e n
eare
st t
enth
.
285.
2915
0262
2
�28�
�5.
3
Ch
eck
Sin
ce 5
2�
25 a
nd
25 i
s cl
ose
to 2
8,th
e an
swer
is
reas
onab
le.
Est
imat
e ea
ch s
qu
are
root
to
the
nea
rest
wh
ole
nu
mb
er.
1.�
3�2
2.�
8�3
3.�
26�5
4.�
41�6
5.�
61�8
6.�
94�10
7.�
152
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850
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a c
alcu
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r to
fin
d e
ach
sq
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e ro
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o th
e n
eare
st t
enth
.
9.�
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410
.�
27�5.
2
11.
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12.
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13.
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5�
10.2
14.
�39
5�
19.9
15.
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6�
29.1
16.
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298
�47
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ENTE
R2n
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NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Est
imat
ing
Sq
uar
e R
oo
ts
Rec
all t
hat
a pe
rfec
t sq
uare
is a
squ
are
of a
rat
iona
l num
ber.
In L
esso
n 5-
8, y
ou le
arne
d th
at a
nynu
mbe
r th
at c
an b
e w
ritte
n as
a f
ract
ion
is a
rat
iona
l num
ber.
A n
umbe
r th
at c
anno
t be
writ
ten
as a
frac
tion
is a
n ir
rati
on
al n
um
ber
.
01
23
45
6
28
©G
lenc
oe/M
cGra
w-H
ill61
3M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
The
Geo
met
ric
Mea
nT
he
squ
are
root
of
the
prod
uct
of
two
nu
mbe
rs i
s ca
lled
th
eir
geom
etri
c m
ean
.T
he
geom
etri
c m
ean
of
12 a
nd
48 i
s �
12�
4�
8��
�57
6�
or 2
4.
Fin
d t
he
geom
etri
c m
ean
for
eac
h p
air
of n
um
ber
s.
1.2
and
84
2.4
and
96
3.9
and
1612
4.16
an
d 4
85.
16 a
nd
3624
6.12
an
d 3
6
7.18
an
d 8
128.
2 an
d 18
69.
27 a
nd
1218
Rec
all
the
defi
nit
ion
of
a ge
omet
ric
seq
uen
ce.E
ach
ter
m i
s fo
un
d by
mu
ltip
lyin
g th
e pr
evio
us
term
by
the
sam
e n
um
ber.
A m
issi
ng
term
in
age
omet
ric
sequ
ence
equ
als
the
geom
etri
c m
ean
of
the
two
term
s on
eit
her
side
.
Fin
d t
he
mis
sin
g te
rm i
n e
ach
geo
met
ric
seq
uen
ce.
10.
4,12
,,1
08,3
2436
11.
10,
,62.
5,15
6.25
,390
.625
25
12.
1,0.
4,,0
.064
,0.0
256
0.16
13.
700,
70,7
,0.7
,,0
.007
0.07
14.
6,,2
412
15.
18,
,32
24?
?
??
??En
richm
ent
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enric
hmen
t
Lesson 11–1
Answers (Lessons 11-1 and 11-2)
© Glencoe/McGraw-Hill A6 Mathematics: Applications and Concepts, Course 2
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice:
Wor
d Pr
oble
ms
Est
imat
ing
Sq
uar
e R
oo
ts
©G
lenc
oe/M
cGra
w-H
ill61
6M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
1.G
EOM
ETRY
Th
e di
amet
er d
of a
cir
cle
wit
h a
rea
Ais
giv
en b
y th
e fo
rmu
la
d�
��4 �A � �.W
hat
is
the
diam
eter
of
a
circ
le w
ith
an
are
a of
56
squ
are
inch
es?
Use
3.1
4 fo
r �
and
rou
nd
to t
he
nea
rest
ten
th.
8.4
in.
2.FE
NC
ING
Car
men
wan
ts t
o bu
y fe
nci
ng
to e
ncl
ose
a sq
uar
e ga
rden
wit
h a
nar
ea o
f 50
0 sq
uar
e fe
et.H
ow m
uch
fen
cin
g do
es C
arm
en n
eed
to b
uy?
Rou
nd
to t
he
nea
rest
ten
th.
89.4
ft
3.O
CEA
NS
Th
e sp
eed
vin
fee
t pe
r se
con
dof
an
oce
an w
ave
in s
hal
low
wat
er o
fde
pth
din
fee
t is
giv
en b
y th
e fo
rmu
lav
��
32d
�.W
hat
is
the
spee
d of
an
ocea
n w
ave
at a
dep
th o
f 10
fee
t?R
oun
d to
th
e n
eare
st t
enth
.17
.9 f
t/s
4.LI
GH
TIN
GA
new
fla
shli
ght
has
a b
eam
wh
ose
wid
th w
at a
dis
tan
ce d
from
th
efl
ash
ligh
t is
giv
en b
y th
e fo
rmu
law
�1.
2�d �.
Wh
at i
s th
e w
idth
of
the
beam
at
a di
stan
ce o
f 30
fee
t? R
oun
d to
the
nea
rest
ten
th.
6.6
ft
5.SO
UN
DT
he
spee
d of
sou
nd
in a
ir c
inm
eter
s pe
r se
con
d at
a t
empe
ratu
re T
in d
egre
es C
elsi
us
is g
iven
appr
oxim
atel
y by
th
e fo
rmu
la
c�
�40
2(T
��
273
�)�.
Wh
at i
s th
e sp
eed
of s
oun
d in
air
at
a te
mpe
ratu
re o
f 25
deg
rees
Cel
siu
s? R
oun
d to
th
en
eare
st t
enth
.34
6.1
m/s
6.PR
OJE
CTI
LES
Th
e m
uzz
le v
eloc
ity
vin
feet
per
sec
ond
nec
essa
ry f
or a
can
non
to h
it a
tar
get
xfe
et a
way
is
esti
mat
edby
th
e fo
rmu
la v
��
32x
�.W
hat
mu
zzle
velo
city
is
requ
ired
to
hit
a t
arge
t3,
000
feet
aw
ay?
Rou
nd
to t
he
nea
rest
ten
th.
309.
8 ft
/s
3,00
0 ft
Lesson 11–2
©G
lenc
oe/M
cGra
w-H
ill61
5M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Est
imat
e ea
ch s
qu
are
root
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nea
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ole
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mb
er.
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985
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125
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alcu
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ach
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.
19.
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om l
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1
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ph �
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d �
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e sa
me
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01
23
45
87
64262
Prac
tice:
Ski
llsE
stim
atin
g S
qu
are
Ro
ots
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Answers (Lesson 11-2)
© Glencoe/McGraw-Hill A7 Mathematics: Applications and Concepts, Course 2
An
swer
s
Wo
rld
Ser
ies
Rec
ord
sE
ach
pro
ble
m g
ives
th
e n
ame
of a
fam
ous
bas
ebal
l p
laye
r.T
o fi
nd
wh
o se
t ea
ch r
ecor
d,g
rap
h t
he
poi
nts
on
th
e n
um
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lin
e.
1.p
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ed 2
3 st
rik
eou
ts i
n o
ne
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ld S
erie
s
Uat
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3.3
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at �3 2�,
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e h
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in h
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pp
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s in
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ld S
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at �1 16 3�
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at 0
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at �
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nd
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orld
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at �
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at 5
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at �
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at 7
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5.42
Wor
ld S
erie
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aree
r
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at �
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NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enric
hmen
t
©G
lenc
oe/M
cGra
w-H
ill61
8M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
KO
UF
AX
04
32
1
48
76
5
JA
CK
SO
N
YO
GI
BE
RR
A
04
32
1
48
76
5
BA
BE
RU
HT
MK
CI
YE
MA
TN
EL
812
1110
9
©G
lenc
oe/M
cGra
w-H
ill61
7M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Pre-
Act
ivit
yC
om
ple
te t
he
Min
i Lab
at
the
top
of
pag
e 47
5 in
yo
ur
text
bo
ok.
Wri
te y
ou
r an
swer
s b
elo
w.
Use
alg
ebra
tile
s to
est
imat
e th
e sq
uar
e ro
ot
of
each
nu
mb
er t
oth
e n
eare
st w
ho
le n
um
ber
.
1.40
62.
285
3.85
94.
628
5.D
escr
ibe
anot
her
met
hod
th
at y
ou c
ould
use
to
esti
mat
e th
e sq
uar
e ro
otof
a n
um
ber.
Sam
ple
an
swer
:sq
uar
e n
um
ber
s u
sin
g g
ues
san
d c
hec
k
Rea
din
g t
he
Less
on
6.W
hy
is �
4�a
rati
onal
nu
mbe
r an
d �
2�an
irr
atio
nal
nu
mbe
r?S
amp
lean
swer
:�
4��
2,an
d 2
can
be
wri
tten
as
a fr
acti
on
:�2 1�.
So
,�
4�is
a r
atio
nal
nu
mb
er.�
2��
1.41
4213
5…,w
hic
h is
no
t an
inte
ger
or
a re
pea
tin
g o
r te
rmin
atin
g d
ecim
al.I
t ca
nn
ot
be
wri
tten
as
a fr
acti
on
.So
,�2�
is a
n ir
rati
on
al n
um
ber
.
7.H
ow d
o yo
u r
ead
the
stat
emen
t �
64��
�75�
��
81�?
Th
e sq
uar
e ro
ot
of
64 is
less
th
an t
he
squ
are
roo
t o
f 75
,wh
ich
is le
ss t
han
the
squ
are
roo
t o
f 81
.
8.W
hy
are
�64�
and
�81�
use
d in
Exa
mpl
e 1?
Sam
ple
an
swer
:64
an
d81
are
per
fect
sq
uar
es,a
nd
th
ey a
re t
he
clo
sest
inte
ger
per
fect
sq
uar
es t
o 7
5.T
hey
are
use
d t
o f
ind
an
est
imat
e fo
rth
e sq
uar
e ro
ot
of
75.
Hel
pin
g Y
ou
Rem
emb
er9.
Th
e ke
y to
est
imat
ing
squ
are
root
s w
ith
out
a ca
lcu
lato
r is
to
be f
amil
iar
wit
h c
omm
on p
erfe
ct s
quar
es.C
ompl
ete
the
foll
owin
g ta
ble
of c
omm
onpe
rfec
t sq
uar
es t
hen
tes
t yo
urs
elf
to s
ee h
ow m
any
you
can
rem
embe
rw
ith
out
usi
ng
a ca
lcu
lato
r.
Read
ing
to L
earn
Mat
hem
atic
sE
stim
atin
g S
qu
are
Ro
ots
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Nu
mb
er5
67
89
1011
1213
1415
1620
25
Sq
uar
e25
3649
6481
100
121
144
169
196
225
256
400
625
Lesson 11–2
Answers (Lesson 11-2)
© Glencoe/McGraw-Hill A8 Mathematics: Applications and Concepts, Course 2
Fin
d t
he
mis
sin
g m
easu
re o
f ea
ch r
igh
t tr
ian
gle.
Rou
nd
to
the
nea
rest
ten
th i
f n
eces
sary
.
1.18
.7 m
2.7.
1 in
.
3.8.
4 ft
4.32
.8 c
m
5.37
.9 in
.6.
1.3
yd
7.9.
5 m
8.15
.5 m
m
9.a
�15
cm
,b�
20 c
m25
cm
10.
a�
2 yd
,b�
12 y
d12
.2 y
d
11.
a�
13 i
n.,
c�
16.5
in
.10
.2 in
.12
.b
�8
mm
,c�
17 m
m15
mm
13.
a�
1.3
ft,b
�4.
6 ft
4.8
ft14
.a
�14
.7 m
,c�
23 m
17.7
m
Det
erm
ine
wh
eth
er e
ach
tri
angl
e w
ith
th
e gi
ven
sid
e le
ngt
hs
is a
righ
t tr
ian
gle.
Wri
te y
esor
no.
15.
10 f
t,24
ft,
26 f
tye
s16
.5
in.,
8 in
.,9
in.
no
17.
6 cm
,9 c
m,1
2 cm
no
18.
4.5
mm
,6.0
mm
,7.5
mm
yes
14 m
mc
mm6.
7 m
m
11.2
m
6 m
a m
2.7
yd3
yd
a yd
20.3
in.
32 in
.
c in
.
20 c
m
26 c
mx
cm12
.4 ft
a ft15
ft
5 in
.
c in
.
5 in
.7
m
b m
20 m
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice:
Ski
llsT
he
Pyt
hag
ore
an T
heo
rem
©G
lenc
oe/M
cGra
w-H
ill62
0M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Lesson 11–3
©G
lenc
oe/M
cGra
w-H
ill61
9M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Fin
d t
he
mis
sin
g m
easu
re o
f a
righ
t tr
ian
gle
if a
�4
inch
es a
nd
b�
3 in
ches
.
c2�
a2�
b2P
ytha
gore
an T
heor
em
c2�
42�
32R
epla
ce a
with
4 a
nd b
with
3.
c2�
16�
9E
valu
ate
42an
d 32
.
c2�
25A
dd.
�c2 �
��
25�Ta
ke t
he s
quar
e ro
ot o
f ea
ch s
ide.
c�
5S
impl
ify.
Th
e le
ngt
h o
f th
e h
ypot
enu
se i
s 5
inch
es.
Det
erm
ine
wh
eth
er a
tri
angl
e w
ith
sid
e le
ngt
hs
of 6
met
ers,
9 m
eter
s,an
d 1
2 m
eter
s is
a r
igh
t tr
ian
gle.
c2�
a2�
b2P
ytha
gore
an T
heor
em
122
�62
�92
Rep
lace
aw
ith 6
, b
with
9,
and
cw
ith 1
2.
144
�36
�81
Sim
plify
.
144
11
7A
dd.
Th
e tr
ian
gle
is n
ota
righ
t tr
ian
gle.
Fin
d t
he
mis
sin
g m
easu
re o
f ea
ch r
igh
t tr
ian
gle.
Rou
nd
to
the
nea
rest
ten
th i
f n
eces
sary
.
1.2.
3.
9.8
in.
9.0
m9.
3 cm
Det
erm
ine
wh
eth
er e
ach
tri
angl
e w
ith
th
e gi
ven
sid
e le
ngt
hs
is a
righ
t tr
ian
gle.
Wri
te y
esor
no.
4.15
ft,
8 ft
,17
ftye
s5.
5 in
.,13
in
.,17
in
.n
o6.
9 yd
,40
yd,4
1 yd
yes
13 c
m
16 c
m
a cm
5 m
7.5
mcm
9 in
.
4 in
.c
in.
3 in
.
4 in
.c
in.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Th
e P
yth
ago
rean
Th
eore
m
The
sid
es o
f a
right
tria
ngle
hav
e sp
ecia
l nam
es.T
he s
ides
adj
acen
t to
the
rig
ht a
ngle
are
the
leg
s.T
he s
ide
oppo
site
the
rig
ht a
ngle
is t
he
c2�
a2�
b2
hyp
ote
nu
se.T
he P
yth
ago
rean
Th
eore
mde
scrib
es t
he r
elat
ions
hip
betw
een
the
leng
th o
f th
e hy
pote
nuse
and
the
leng
ths
of t
he le
gs.I
n a
right
tria
ngle
, th
e sq
uare
of
the
leng
th o
f th
e hy
pote
nuse
equ
als
the
sum
of
the
squa
res
of t
he le
ngth
s of
the
legs
.b
ac
Answers (Lesson 11-3)
© Glencoe/McGraw-Hill A9 Mathematics: Applications and Concepts, Course 2
An
swer
s
Pre-
Act
ivit
yR
ead
th
e in
tro
du
ctio
n a
t th
e to
p o
f p
age
479
in y
ou
r te
xtb
oo
k.W
rite
yo
ur
answ
ers
bel
ow
.
1.C
an t
he
mir
ror
fit
thro
ugh
th
e do
orw
ay?
Exp
lain
.It
will
no
t fi
t if
th
em
irro
r is
ho
rizo
nta
l or
vert
ical
.It
may
fit
if it
is t
ilted
.
2.M
ake
a sc
ale
draw
ing
on g
rid
pape
r to
sol
ve t
he
prob
lem
.S
amp
le a
nsw
er:T
he
mir
ror
will
fit
if it
is t
urn
ed,
sin
ce t
her
e is
mo
re t
han
7 f
eet
of
spac
eb
etw
een
op
po
site
co
rner
s o
f th
e d
oo
r.
Rea
din
g t
he
Less
on
3.In
th
e P
yth
agor
ean
Th
eore
m c
2�
a2�
b2,w
hic
h l
ette
r re
pres
ents
the
len
gth
of
the
hyp
oten
use
?c
4.H
ow d
o yo
u k
now
th
at t
he
diag
onal
of
a re
ctan
gle
is t
he
hyp
oten
use
of
two
righ
t tr
ian
gles
?S
amp
le a
nsw
er:
A r
ecta
ng
le h
as f
ou
r ri
gh
tan
gle
s.
5.In
Exa
mpl
es 4
an
d 5
on p
age
481,
how
do
you
kn
ow w
hic
h l
engt
h i
s c?
Sam
ple
an
swer
:c
is t
he
hyp
ote
nu
se,w
hic
h is
alw
ays
the
lon
ges
t o
f th
e th
ree
sid
es o
f a
rig
ht
tria
ng
le.
Hel
pin
g Y
ou
Rem
emb
er6.
Su
mm
ariz
e w
hat
you
lea
rned
in
th
is l
esso
n b
y la
beli
ng
the
side
s of
th
eri
ght
tria
ngl
e w
ith
th
e le
tter
s a,
b,an
d c
and
then
com
plet
ing
the
tabl
e.
a
b
c
6.5
ft7.
2 ft
3 ft
1 sq
uar
e =
1 ft
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Read
ing
to L
earn
Mat
hem
atic
sT
he
Pyt
hag
ore
an T
heo
rem
©G
lenc
oe/M
cGra
w-H
ill62
2M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
You
can
fin
d
If y
ou k
now
the
len
gth
s
ab
,c
ba,
c
ca,
b
©G
lenc
oe/M
cGra
w-H
ill62
1M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Prac
tice:
Wor
d Pr
oble
ms
Th
e P
yth
ago
rean
Th
eore
m
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Lesson 11–3
1.O
RIG
AM
IC
hee
has
a p
iece
of
pape
rm
easu
rin
g 8.
5 in
ches
by
8.5
inch
es.I
fsh
e fo
lds
the
pape
r di
agon
ally
in
hal
f,h
ow l
ong
is t
he
fold
ed s
ide?
Rou
nd
toth
e n
eare
st t
enth
.12
.0 in
.
2.C
OM
PUTE
RS
In a
com
pute
r ca
talo
g,a
com
pute
r m
onit
or i
s sa
id t
o be
19
in
ches
.Th
is d
ista
nce
is
the
diag
onal
dist
ance
acr
oss
the
scre
en.I
f th
e sc
reen
is 1
0 in
ches
hig
h,w
hat
is
the
wid
th o
fth
e sc
reen
? R
oun
d to
th
e n
eare
st t
enth
.16
.2 in
.
3.A
NTE
NN
AS
A w
ire
10 m
eter
s lo
ng
issu
ppor
tin
g a
uti
lity
pol
e.T
he
wir
e is
anch
ored
to
the
grou
nd
and
is a
ttac
hed
to t
he
pole
9 m
eter
s ab
ove
the
grou
nd.
Wh
at i
s th
e di
stan
ce f
rom
th
e bo
ttom
of
the
pole
to
the
poin
t w
her
e th
e w
ire
isat
tach
ed t
o th
e gr
oun
d? R
oun
d to
th
en
eare
st t
enth
.4.
4 m
9 m
10 m
x m
4.R
AM
PSC
ryst
al w
ants
to
buil
d a
ram
pth
at w
ill
rise
4 f
eet
over
a h
oriz
onta
ldi
stan
ce o
f 20
fee
t.H
ow l
ong
wil
l th
era
mp
be?
Rou
nd
to t
he
nea
rest
ten
th.
20.4
ft
4 ft
20 ft
x ft
5.PO
OLS
Sal
omon
sw
ims
diag
onal
lyac
ross
his
poo
l ev
ery
day.
If S
alom
on’s
pool
is
4 m
eter
s w
ide
and
16 m
eter
sdi
agon
ally
acr
oss,
how
lon
g is
his
poo
l,to
th
e n
eare
st t
enth
of
a m
eter
?15
.5 m
6.FR
AM
ESR
osa
has
a p
ictu
re f
ram
e th
atm
easu
res
12 i
nch
es b
y 18
in
ches
.Wh
atis
th
e di
agon
al d
ista
nce
acr
oss
the
fram
e? R
oun
d to
th
e n
eare
st t
enth
.21
.6 in
.
Answers (Lesson 11-3)
© Glencoe/McGraw-Hill A10 Mathematics: Applications and Concepts, Course 2
©G
lenc
oe/M
cGra
w-H
ill62
4M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Fin
d t
he
area
of
a p
aral
lelo
gram
if
the
bas
e
is 6
in
ches
an
d t
he
hei
ght
is 3
.7 i
nch
es.
Est
imat
eA
�6
�4
or 2
4 in
2
A�
bhA
rea
of a
par
alle
logr
am
A�
6�
3.7
Rep
lace
b w
ith 6
and
hw
ith 3
.7.
A�
22.2
Mul
tiply
.
Th
e ar
ea o
f th
e pa
rall
elog
ram
is
22.2
squ
are
inch
es.T
his
is c
lose
to
the
estim
ate.
Fin
d t
he
area
of
the
par
alle
logr
am a
t th
e ri
ght.
Est
imat
eA
�10
�10
or
100
cm2
A�
bhA
rea
of a
par
alle
logr
am
A�
12 �
8R
epla
ce b
with
12
and
hw
ith 8
.
A�
96M
ultip
ly.
Th
e ar
ea o
f th
e pa
rall
elog
ram
is
96 s
quar
e ce
nti
met
ers.
Thi
s is
clo
se t
o th
e es
timat
e.
Fin
d t
he
area
of
each
par
alle
logr
am.R
oun
d t
o th
e n
eare
st t
enth
if
nec
essa
ry.
1.2.
3.
66 f
t236
.8 m
m2
272
in2
17 in
.
16 in
.
4.6
mm
8 m
m
5 ft
13.2
ft
12 c
m
8 cm3.
7 in
.
6 in
.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Are
a o
f P
aral
lelo
gra
ms
The
are
a A
of a
par
alle
logr
am e
qual
s th
e pr
oduc
t of
its
base
ban
d its
hei
ght
h.
A�
bh
The
base
is a
ny s
ide
of a
par
alle
logr
am.
The
heig
ht is
the
leng
th o
fth
e se
gmen
t per
pend
icul
arto
the
base
with
end
poin
tson
opp
osite
sid
es.
b
h
©G
lenc
oe/M
cGra
w-H
ill62
3M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Pyth
ago
ras
in t
he
Air
In t
he
diag
ram
at
the
righ
t,an
air
plan
e h
eads
nor
th a
t 18
0 m
i/h.
Bu
t,th
e w
ind
is b
low
ing
tow
ards
th
e ea
st a
t 30
mi/h
.So,
the
airp
lan
e is
rea
lly
trav
elin
g ea
st o
f n
orth
.Th
e m
iddl
e ar
row
in
th
edi
agra
m s
how
s th
e ac
tual
dir
ecti
on o
f th
e ai
rpla
ne.
Th
e ac
tual
spe
ed o
f th
e pl
ane
can
be
fou
nd
usi
ng
the
Pyt
hag
orea
nT
heo
rem
.
�30
2�
�18
02�
��
900
��
32,4
0�
0�
��
33,3
0�
0�
�18
2.5
Th
e pl
ane’
s ac
tual
spe
ed i
s ab
out
182.
5 m
i/h.
Fin
d t
he
actu
al s
pee
d o
f ea
ch a
irp
lan
e.R
oun
d a
nsw
ers
to t
he
nea
rest
ten
th.(
You
mig
ht
wis
h t
o d
raw
a d
iagr
am t
o h
elp
you
sol
ve t
he
pro
ble
m.)
1.A
n a
irpl
ane
trav
els
at 2
40 m
i/h e
ast.
2.A
n a
irpl
ane
trav
els
at 6
20 m
i/h w
est.
A w
ind
is b
low
ing
at 2
0 m
i/h t
owar
dA
win
d is
blo
win
g at
35
mi/h
tow
ard
the
sou
th.
240.
8 m
i/hth
e so
uth
.62
1.0
mi/h
3.A
n a
irpl
ane
trav
els
at 4
50 m
i/h s
outh
.4.
An
air
plan
e tr
avel
s at
1,2
00 m
i/h e
ast.
A w
ind
is b
low
ing
at 4
0 m
i/h t
owar
dA
win
d is
blo
win
g at
30
mi/h
tow
ard
the
east
.45
1.8
mi/h
the
nor
th.
1,20
0.4
mi/h
Enric
hmen
tN
AM
E__
____
____
____
____
____
____
____
____
____
__D
ATE
___
____
____
___
PE
RIO
D
____
_ E
N(n
ot d
raw
n to
sca
le)
180
mi/h
30 m
i/h
Lesson 11–3
Answers (Lessons 11-3 and 11-4)
© Glencoe/McGraw-Hill A11 Mathematics: Applications and Concepts, Course 2
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice:
Wor
d Pr
oble
ms
Are
a o
f P
aral
lelo
gra
ms
©G
lenc
oe/M
cGra
w-H
ill62
6M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
1.SA
ILS
Joyc
e w
ants
to
con
stru
ct a
sai
lw
ith
th
e di
men
sion
s sh
own
.How
mu
chm
ater
ial
wil
l be
use
d?35
0 ft
2
14 ft25
ft
2.SI
GN
SP
edro
wan
ts t
o m
ake
the
sign
in
the
shap
e sh
own
an
d n
eeds
to
know
how
mu
ch m
ater
ial
wil
l be
nee
ded.
Wh
at i
s th
e ar
ea o
f th
e si
gn?
1,05
0 in
2 30 in
.
35 in
.
Yard
Sale
3.SH
AD
ING
Alm
a’s
engi
nee
rin
g fi
rm m
ust
dete
rmin
e th
e ar
ea o
f th
e la
rges
tn
oon
tim
e sh
adow
th
at a
pro
pose
dbu
ildi
ng
desi
gn w
ill
crea
te.W
hat
is
the
area
of
the
shad
ow?
2,24
0 ft
2
40 ft
56 ft
4.PO
OLS
Tam
ika
has
des
ign
ed a
poo
l in
the
shap
e sh
own
.Wh
at i
s th
e ar
ea o
fth
e bo
ttom
of
the
pool
if
the
surf
ace
ispe
rfec
tly
flat
?60
0 m
2
30 m
20 m
5.C
ITY
PLA
NN
ING
Tw
o pa
rall
el s
tree
ts a
recu
t ac
ross
by
two
oth
er p
aral
lel
stre
ets
as s
how
n i
n t
he
figu
re,c
utt
ing
off
apa
rcel
of
lan
d in
th
e sh
ape
of a
para
llel
ogra
m.F
ind
the
area
of
the
parc
el o
f la
nd.
85,0
00 f
t2
250
ft
340
ft
Mai
n St
reet
Dres
den
Way
Columbus Ave.
Jefferson Ave.
6.TA
RPS
Nek
a w
ants
to
cut
a ta
rp i
n t
he
shap
e sh
own
.Wh
at i
s th
e m
inim
um
amou
nt
of c
anva
s cl
oth
th
at h
e w
ill
nee
d?1,
440
ft2
36 ft
40 ft
Lesson 11–4
©G
lenc
oe/M
cGra
w-H
ill62
5M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Fin
d t
he
area
of
each
par
alle
logr
am.R
oun
d t
o th
e n
eare
st t
enth
if
nec
essa
ry.
1.ba
se �
5 ft
2.ba
se �
9 in
.h
eigh
t �
12 f
t60
ft2
hei
ght
�2
in.
18 in
2
3.ba
se �
6 cm
4.ba
se �
4 �2 5�
yd
hei
ght
�5.
5 cm
33 c
m2
hei
ght
�2
yd8 �
4 5�yd
2
5.ba
se �
15.3
mm
6.ba
se �
19.6
mh
eigh
t �
8 m
m12
2.4
mm
2h
eigh
t �
14.5
m28
4.2
m2
7.6
cm2
8.28
in2
9.16
5 m
m2
10.
108
ft2
11.
4.6
cm2
12.
236
in2
13.
51.6
mm
214
.50
4 ft
2o
r 56
yd
2
7 yd
24 ft
4.3
mm
12 m
m
20 in
. 11
in.
4 5
2.3
cm
2 cm
12 ft
9 ft
15 m
m
11 m
m
7 in
.
4 in
.
2 cm
3 cmPr
actic
e: S
kills
Are
a o
f P
aral
lelo
gra
ms
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Answers (Lesson 11-4)
© Glencoe/McGraw-Hill A12 Mathematics: Applications and Concepts, Course 2
Two
Are
a Pu
zzle
sC
ut
out
the
five
pu
zzle
pie
ces
at t
he
bot
tom
of
this
pag
e.T
hen
use
them
to
solv
e th
ese
two
pu
zzle
s.
1.U
se a
ll f
ive
puzz
le p
iece
s to
mak
e2.
Use
th
e fo
ur
larg
est
piec
es t
o m
ake
a sq
uar
e w
ith
an
are
a of
9 s
quar
ea
squ
are
wit
h a
n a
rea
of 8
squ
are
inch
es.R
ecor
d yo
ur
solu
tion
bel
ow.
inch
es.R
ecor
d yo
ur
solu
tion
bel
ow.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enric
hmen
t
©G
lenc
oe/M
cGra
w-H
ill62
8M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
2 in
.
1 in
.
1 in
.
2 in
.
2 in
.
1 in
2
©G
lenc
oe/M
cGra
w-H
ill62
7M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Pre-
Act
ivit
yC
om
ple
te t
he
Min
i Lab
at
the
top
of
pag
e 48
3 in
yo
ur
text
bo
ok.
Wri
te y
ou
r an
swer
s b
elo
w.
1.W
hat
is
the
valu
e of
xan
d y
for
each
par
alle
logr
am?
x�
4 u
nit
s,y
�2
un
its
2.C
oun
t th
e gr
id s
quar
es t
o fi
nd
the
area
of
each
par
alle
logr
am.
8 sq
un
its
3.O
n g
rid
pape
r,dr
aw t
hre
e di
ffer
ent
para
llel
ogra
ms
in w
hic
h x
�5
un
its
and
y�
4 u
nit
s.F
ind
the
area
of
each
.
Th
e ar
ea o
f ea
ch is
20
sq u
nit
s.4.
Mak
e a
con
ject
ure
abou
t h
ow t
o fi
nd
the
area
of
a pa
rall
elog
ram
if
you
know
th
e va
lues
of
xan
d y.
Th
e ar
ea e
qu
als
x�
y.
Rea
din
g t
he
Less
on
5.E
xpla
in h
ow t
o fi
nd
the
hei
ght
of a
par
alle
logr
am.
Sam
ple
an
swer
:D
raw
ase
gm
ent
per
pen
dic
ula
r to
th
e b
ase
wit
h e
nd
po
ints
on
op
po
site
sid
es o
f th
e p
aral
lelo
gra
m.T
he
hei
gh
t is
th
e le
ng
th o
f th
is s
egm
ent.
6.S
upp
ose
you
are
ask
ed t
o fi
nd
the
area
of
the
para
llel
ogra
m b
elow
.Is
the
give
n s
olu
tion
cor
rect
? E
xpla
in.
A�
bhA
�12
�5
A�
60T
he
area
of
the
para
llel
ogra
m i
s 60
squ
are
cen
tim
eter
s.S
amp
le a
nsw
er:T
he
area
was
fo
un
d u
sin
g t
he
len
gth
of
the
sid
e o
f th
ep
aral
lelo
gra
m in
stea
d o
f th
e h
eig
ht.
Th
e co
rrec
t an
swer
is 3
6 cm
2 .
Hel
pin
g Y
ou
Rem
emb
er7.
Bec
ause
rec
tan
gles
,rh
ombu
ses,
and
squ
ares
are
all
par
alle
logr
ams,
the
form
ula
for
fin
din
g th
e ar
ea o
f a
para
llel
ogra
m i
s al
so u
sed
to f
ind
the
area
s of
eac
h o
f th
ese
figu
res.
Th
ink
of a
way
to
rem
embe
r th
at t
he
area
of a
par
alle
logr
am i
s th
e pr
odu
ct o
f it
s ba
se a
nd
hei
ght.
For
exa
mpl
e,dr
aw s
ever
al p
aral
lelo
gram
s,re
ctan
gles
,rh
ombu
ses,
and
squ
ares
an
dla
bel
the
base
an
d h
eigh
t fo
r ea
ch.W
rite
th
e fo
rmu
la f
or t
he
area
bel
owea
ch m
odel
.S
ee s
tud
ents
’wo
rk.
3 cm
5 cm
12 c
m
4 51
squ
are
= 1
ft
4
51
squ
are
= 1
ft
4
51
squ
are
= 1
ft
Read
ing
to L
earn
Mat
hem
atic
sA
rea
of
Par
alle
log
ram
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Lesson 11–4
Answers (Lesson 11-4)
© Glencoe/McGraw-Hill A13 Mathematics: Applications and Concepts, Course 2
An
swer
s
Fin
d t
he
area
of
each
fig
ure
.Rou
nd
to
the
nea
rest
ten
th i
f n
eces
sary
.
1.45
cm
22.
3 ft
2
3.15
0 m
m2
4.19
ft2
5.39
.2 c
m2
6.24
8.4
mm
2
7.27
0.6
ft2
8.19
.3 in
2
9.45
.8 c
m2
10.
136.
2 m
m2
11.
tria
ngl
e:ba
se �
16 c
m,h
eigh
t �
9.4
cm75
.2 c
m2
12.
tria
ngl
e:ba
se �
13.5
in
.,h
eigh
t �
6.4
in.
43.2
in2
13.
trap
ezoi
d:ba
ses
22.8
mm
an
d 19
.7 m
m,h
eigh
t 36
mm
765
mm
2
14.
trap
ezoi
d:ba
ses
5 ft
an
d 3 �
1 2�yd
,hei
ght
7 ft
54.3
ft2
14 m
m
3.8
mm
15.3
mm
7.5
cm
12.2
cm
5.6
in.
6.9
in.
12 ft
20.1
ft
25 ft
24 m
m
20.7
mm
7 cm
9.2
cm 2 cm
4 ft3
ft
6.5
ft
12 m
m
18 m
m
10 m
m
3 ft
2 ft
10 c
m
9 cm
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice:
Ski
llsA
rea
of T
rian
gle
s an
d T
rap
ezo
ids
©G
lenc
oe/M
cGra
w-H
ill63
0M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Lesson 11–5
©G
lenc
oe/M
cGra
w-H
ill62
9M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Fin
d t
he
area
of
the
tria
ngl
e.E
stim
ate
�1 2�(6)
(5)
�15
A�
�1 2�bh
Are
a of
a t
riang
le
A�
�1 2�6�
4.5
Rep
lace
bw
ith 6
and
hw
ith 4
.5.
A�
13.5
Mul
tiply
.
Th
e ar
ea o
f th
e tr
ian
gle
is 1
3.5
squ
are
inch
es.T
his
is c
lose
to
the
estim
ate.
Fin
d t
he
area
of
the
trap
ezoi
d.
A�
�1 2�h(b
1�
b 2)
Are
a of
a t
rape
zoid
A�
�1 2�(4)
(3�
6)R
epla
ce h
with
4,
b 1w
ith 3
, an
d b 2
with
6.
A�
18S
impl
ify.
Th
e ar
ea o
f th
e tr
apez
oid
is 1
8 sq
uar
e ce
nti
met
ers.
Fin
d t
he
area
of
each
fig
ure
.Rou
nd
to
the
nea
rest
ten
th i
f n
eces
sary
.
1.2.
3.4.
42 f
t231
.5 m
m2
52.5
in2
175.
5 cm
2
8 cm
13.5
cm
18 c
m
7 in
.5 in
.
14 in
.
7 m
m
9 m
m12
ft7 ft
4 cm
3 cm
6 cm
4.5
in.
6 in
.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Are
a o
f Tri
ang
les
and
Tra
pez
oid
s
The
are
a A
of a
tria
ngle
equ
als
half
the
prod
uct
of it
s ba
se b
and
its h
eigh
t h.
A�
�1 2�bh
A t
rape
zoid
has
tw
o ba
ses,
b1
and
b 2.T
he h
eigh
t of
a t
rape
zoid
is t
he
dist
ance
bet
wee
n th
e tw
o ba
ses.
The
are
a A
of a
tra
pezo
id e
qual
s ha
lf th
e pr
oduc
t of
the
hei
ght
han
d th
e su
m o
f th
e ba
ses
b 1an
d b 2
.
A�
�1 2�h(b
1�
b 2)
b 1 b 2
h
The
base
of a
trian
gle
can
bean
y of
its
side
s.
The
heig
ht is
the
dist
ance
from
a b
ase
to th
e op
posi
te v
erte
x.
b
h
Answers (Lesson 11-5)
© Glencoe/McGraw-Hill A14 Mathematics: Applications and Concepts, Course 2
Pre-
Act
ivit
yC
om
ple
te t
he
Min
i Lab
at
the
top
of
pag
e 48
9 in
yo
ur
text
bo
ok.
Wri
te y
ou
r an
swer
s b
elo
w.
1.W
hat
is
the
area
of
the
para
llel
ogra
m?
24 s
q u
nit
s
2.C
ut
alon
g th
e di
agon
al.W
hat
is
tru
e ab
out
the
tria
ngl
es f
orm
ed?
Th
eyar
e co
ng
ruen
t.
3.W
hat
is
the
area
of
each
tri
angl
e?12
sq
un
its
4.If
th
e ar
ea o
f a
para
llel
ogra
m i
s bh
,th
en w
rite
an
exp
ress
ion
for
th
e ar
eaA
of e
ach
of
the
two
con
gru
ent
tria
ngl
es t
hat
for
m t
he
para
llel
ogra
m.
A =
�1 2�bh
Rea
din
g t
he
Less
on
5.In
a t
rian
gle,
wh
ich
sid
e is
th
e ba
se?
Sam
ple
an
swer
:Th
e b
ase
can
be
any
sid
e o
f th
e tr
ian
gle
.
6.H
ow d
o yo
u f
ind
the
hei
ght
of a
tri
angl
e?S
amp
le a
nsw
er:
On
ceyo
u k
no
w w
hic
h s
ide
is t
he
bas
e,fi
nd
th
e d
ista
nce
fro
m t
he
bas
e to
th
e o
pp
osi
te v
erte
x.
7.F
or w
hat
kin
d of
tri
angl
e m
igh
t th
e h
eigh
t be
fou
nd
outs
ide
of t
he
tria
ngl
e?o
btu
se t
rian
gle
8.H
ow i
s th
e h
eigh
t of
a t
rape
zoid
sim
ilar
to
the
hei
ght
of a
tri
angl
e or
para
llel
ogra
m?
Sam
ple
an
swer
:It
is p
erp
end
icu
lar
to t
he
bas
e.
Hel
pin
g Y
ou
Rem
emb
er9.
Th
e M
ini
Lab
in
th
is l
esso
n g
ave
you
a g
ood
way
to
rem
embe
r th
efo
rmu
la f
or t
he
area
of
a tr
ian
gle
by s
how
ing
you
th
at i
t is
hal
f th
e ar
eaof
a p
aral
lelo
gram
,so
A�
�1 2�bh
.Th
ink
of a
way
to
hel
p yo
u r
emem
ber
the
form
ula
for
th
e ar
ea o
f a
trap
ezoi
d.D
o yo
u r
ecog
niz
e an
yth
ing
in t
he
form
ula
A�
�1 2�h(b
1�
b 2)?
Sam
ple
an
swer
:F
ind
ing
�1 2�(b
1�
b2)
mea
ns
to f
ind
th
e av
erag
e o
f th
e le
ng
ths
of
the
bas
es.S
o,
the
area
of
a tr
apez
oid
is t
he
pro
du
ct o
f th
e av
erag
e o
f th
ele
ng
ths
of
the
bas
es t
imes
th
e h
eig
ht.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Read
ing
to L
earn
Mat
hem
atic
sA
rea
of T
rian
gle
s an
d T
rap
ezo
ids
©G
lenc
oe/M
cGra
w-H
ill63
2M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
©G
lenc
oe/M
cGra
w-H
ill63
1M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Prac
tice:
Wor
d Pr
oble
ms
Are
a o
f Tri
ang
les
and
Tra
pez
oid
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Lesson 11–5
1.G
EOG
RA
PHY
Ark
ansa
s h
as a
sh
ape
that
is s
imil
ar t
o a
trap
ezoi
d w
ith
bas
es o
fab
out
182
mil
es a
nd
267
mil
es a
nd
ah
eigh
t of
abo
ut
254
mil
es.E
stim
ate
the
area
of
the
stat
e.57
,023
mi2
2.PA
TIO
SG
reta
is
mak
ing
a pa
tio
wit
hth
e di
men
sion
s gi
ven
in
th
e fi
gure
.W
hat
is
the
area
of
the
pati
o?
172.
5 ft
215 ft
15 ft
8 ft
3.FL
AG
SM
alil
a w
ants
to
mak
e th
eIn
tern
atio
nal
Mar
ine
Sig
nal
fla
g sh
own
wh
ich
rep
rese
nts
th
e n
um
ber
six.
Wh
atis
th
e ar
ea o
f th
e fl
ag?
1,75
0 in
2
30 in
.10
0 in
.5
in.
4.SI
GN
SE
stim
ate
the
area
of
the
yiel
dsi
gn.
390
in2
30 in
.
26 in
.
5.TI
LIN
GA
cer
amic
s co
mpa
ny
wan
ts t
opr
odu
ce t
iles
in
th
e sh
ape
show
n.W
hat
is t
he
area
of
the
surf
ace
of e
ach
til
e?
36.1
25 c
m2
8.5
cm
8.5
cm
6.G
AR
DEN
ING
Kin
u w
ants
to
buy
tops
oil
for
a se
ctio
n o
f h
er g
arde
n t
hat
has
th
edi
men
sion
s sh
own
in
th
e fi
gure
.Wh
atis
th
e ar
ea o
f th
is s
ecti
on o
f K
inu
’sga
rden
?
7 yd
2
4 yd
3.5
yd 4 yd
Answers (Lesson 11-5)
© Glencoe/McGraw-Hill A15 Mathematics: Applications and Concepts, Course 2
An
swer
s
©G
lenc
oe/M
cGra
w-H
ill63
4M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Fin
d t
he
area
of
the
circ
le.
A�
�r2
Are
a of
circ
le
A�
��
52R
epla
ce r
with
5.
578
.539
8163
4
Th
e ar
ea o
f th
e ci
rcle
is
appr
oxim
atel
y 78
.5 s
quar
e ce
nti
met
ers.
Fin
d t
he
area
of
a ci
rcle
th
at h
as a
dia
met
er o
f 9.
4 m
illi
met
ers.
A�
�r2
Are
a of
a c
ircle
A�
��
4.72
Rep
lace
rw
ith 9
.4
2 or
4.7
.
A�
69.4
Use
a c
alcu
lato
r.
Th
e ar
ea o
f th
e ci
rcle
is
appr
oxim
atel
y 69
.4 s
quar
e m
illi
met
ers.
Fin
d t
he
area
of
each
cir
cle.
Rou
nd
to
the
nea
rest
ten
th.
1.2.
3.
153.
9 in
249
0.9
mm
245
2.4
ft2
4.ra
diu
s �
2.6
cm5.
radi
us
�14
.3 i
n.
6.di
amet
er �
5 �1 2�
yd
21.2
cm
264
2.4
in2
23.8
yd
2
7.di
amet
er �
4�3 4�
mi
8.di
amet
er �
7.9
mm
9.ra
diu
s �
2 �1 5�
ft
17.7
mi2
49.0
mm
215
.2 f
t2
12 ft
25 m
m7
in.
ENTE
R�
�
5 c
m
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Are
a o
f C
ircl
es
The
are
a A
of a
circ
le e
qual
s th
e pr
oduc
t of
pi (
�)
and
the
squa
re o
f its
rad
ius
r.
A�
�r2
©G
lenc
oe/M
cGra
w-H
ill63
3M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Her
on
’s F
orm
ula
A f
orm
ula
nam
ed a
fter
Her
on o
f Ale
xan
dria
,Egy
pt,c
an b
e u
sed
to f
ind
the
area
of
a tr
ian
gle
give
n t
he
len
gth
s of
its
sid
es.
Her
on’s
for
mu
last
ates
th
at t
he
area
Aof
a t
rian
gle
wh
ose
side
s m
easu
rea,
b,an
d c
is g
iven
by
A�
�s(
s�a
�)(
s�b)
�(s
�c)
�,
wh
ere
sis
th
e se
mip
erim
eter
:
s�
�a�
2b�
c�
.
1–6
Est
imat
es w
ill v
ary.
Est
imat
e th
e ar
ea o
f ea
ch t
rian
gle
by
fin
din
g th
e m
ean
of
the
inn
eran
d o
ute
r m
easu
res.
Th
en u
se H
eron
’s F
orm
ula
to
com
pu
te a
mor
eex
act
area
.Giv
e ea
ch a
nsw
er t
o th
e n
eare
st t
enth
of
a sq
uar
e u
nit
.
1.2.
3.
Est
imat
ed a
rea:
15E
stim
ated
are
a:38
Est
imat
ed a
rea:
25
Com
pute
d ar
ea:
15.6
Com
pute
d ar
ea:
37.4
Com
pute
d ar
ea:
24
4.5.
6.
Est
imat
ed a
rea:
20.5
Est
imat
ed a
rea:
12.5
Est
imat
ed a
rea:
18
Com
pute
d ar
ea:
21.2
Com
pute
d ar
ea:
11.8
Com
pute
d ar
ea:
17.4
9
57
8
83
7 77
6
8
109
9
106
66
Enric
hmen
tN
AM
E__
____
____
____
____
____
____
____
____
____
__D
ATE
___
____
____
___
PE
RIO
D
____
_
Lesson 11–5
Answers (Lessons 11-5 and 11-6)
© Glencoe/McGraw-Hill A16 Mathematics: Applications and Concepts, Course 2
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice:
Wor
d Pr
oble
ms
Are
a o
f C
ircl
es
©G
lenc
oe/M
cGra
w-H
ill63
6M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
1.PO
OLS
Su
san
des
ign
ed a
cir
cula
r po
olw
ith
a d
iam
eter
of
25 m
eter
s.W
hat
is
the
area
of
the
bott
om o
f th
e po
ol?
Rou
nd
to t
he
nea
rest
ten
th.
490.
9 m
2
2.M
ON
EYF
ind
the
area
of
the
coin
to
the
nea
rest
ten
th.
283.
5 m
m2
19 m
m
3.D
RU
MS
Wh
at i
s th
e ar
ea o
f th
edr
um
hea
d on
th
e dr
um
sh
own
bel
ow?
Rou
nd
to t
he
nea
rest
ten
th.
153.
9 in
214 in
.
4.PI
ZZA
Est
imat
e th
e ar
ea o
f th
e to
p of
aro
un
d pi
zza
that
has
a d
iam
eter
of
16 i
nch
es.R
oun
d to
th
e n
eare
st t
enth
.20
1.1
in2
5.G
AR
DEN
ING
Jan
e n
eeds
to
buy
mu
lch
for
the
gard
en w
ith
th
e di
men
sion
ssh
own
in
th
e fi
gure
.For
how
mu
ch a
rea
does
Jan
e n
eed
to b
uy
mu
lch
? R
oun
d to
the
nea
rest
ten
th. 95
.0 y
d2
5.5
yd
6.U
TILI
TIES
Wh
at i
s th
e ar
ea o
f th
e to
psu
rfac
e of
a c
ircu
lar
man
hol
e co
ver
that
has
a r
adiu
s of
30
cen
tim
eter
s? R
oun
dto
th
e n
eare
st t
enth
.2,
827.
4 cm
2Lesson 11–6
©G
lenc
oe/M
cGra
w-H
ill63
5M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Fin
d t
he
area
of
each
cir
cle.
Rou
nd
to
the
nea
rest
ten
th.
1.3.
1 cm
22.
12.6
yd
2
3.96
2.1
mm
24.
615.
8 in
2
5.14
.5 f
t26.
50.3
cm
2
7.69
.4 y
d2
8.1,
590.
4 in
2
9.3.
5 m
m2
10.
444.
9 ft
2
11.
radi
us
�5.
7 m
m12
.ra
diu
s �
8.2
ft10
2.1
mm
221
1.2
ft2
13.
diam
eter
�3 �
1 4�in
.14
.di
amet
er �
15.6
cm
8.3
in2
191.
1 cm
2
15.
radi
us
�1.
1 in
.16
.di
amet
er �
12�3 4�
yd3.
8 in
212
7.7
yd2
11.9
ft2.
1 m
m
22.5
in.
4.7
yd
8 cm
4.3
ft
14 in
.35
mm
4 yd
1 cm
Prac
tice:
Ski
llsA
rea
of
Cir
cles
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Answers (Lesson 11-6)
© Glencoe/McGraw-Hill A17 Mathematics: Applications and Concepts, Course 2
An
swer
s
Seki
Ko
wa
Japa
nes
e m
ath
emat
icia
n S
eki
Kow
a (c
.164
2–17
08)
is c
alle
d T
he
Ari
thm
etic
al S
age
beca
use
of
his
man
y co
ntr
ibu
tion
s to
th
e de
velo
pmen
t of
mat
hem
atic
s in
Jap
an.B
efor
e S
eki,
mat
hem
atic
s in
Jap
an w
as
con
side
red
a fo
rm o
f ar
t to
be
enjo
yed
by i
nte
llec
tual
s in
th
eir
leis
ure
ti
me.
Sek
i de
mon
stra
ted
the
prac
tica
l u
ses
of m
ath
emat
ics
and
intr
odu
ced
soci
al r
efor
ms
that
mad
e it
pos
sibl
e fo
r an
yon
e,n
ot ju
st
inte
llec
tual
s,to
stu
dy m
ath
emat
ics.
On
e of
Sek
i’s c
ontr
ibu
tion
s to
mat
hem
atic
s w
as h
is c
alcu
lati
on o
f a
valu
eof
�th
at w
as c
orre
ct t
o ei
ghte
en d
ecim
al p
lace
s.
��
3.14
1592
6535
8979
3238
…
Sek
i h
ad n
otic
ed t
he
phen
omen
on t
hat
you
see
at
the
righ
t:as
th
en
um
ber
of s
ides
of
a re
gula
r po
lygo
n i
ncr
ease
s,th
e po
lygo
n l
ooks
mor
e an
d m
ore
like
a c
ircl
e.S
o,S
eki
calc
ula
ted
the
foll
owin
g ra
tio
for
poly
gon
s of
in
crea
sin
gly
man
y si
des.
As
the
nu
mbe
r of
sid
es o
f th
e po
lygo
n g
ets
larg
er,t
his
rat
io m
ust
get
clos
er t
o th
e ra
tio
of t
he
circ
um
fere
nce
of
the
circ
le t
o th
e di
amet
er o
fth
e ci
rcle
.Th
is r
atio
,of
cou
rse,
is �
.
You
are
giv
en i
nfo
rmat
ion
bel
ow a
bou
t a
regu
lar
pol
ygon
an
d t
he
circ
le d
raw
n a
rou
nd
th
e p
olyg
on.U
se a
cal
cula
tor
to f
ind
Sek
i’sra
tio.
(Giv
e as
man
y d
ecim
al p
lace
s as
th
ere
are
in y
our
calc
ula
tor
dis
pla
y.)
Wh
at d
o yo
u n
otic
e ab
out
you
r an
swer
s?
1.le
ngt
h o
f on
e si
de �
52.
len
gth
of
one
side
�4.
5922
nu
mbe
r of
sid
es �
6n
um
ber
of s
ides
�8
diam
eter
of
circ
le �
10di
amet
er o
f ci
rcle
�12
33.
0614
6666
7
3.le
ngt
h o
f on
e si
de �
3.75
444.
len
gth
of
one
side
�37
.544
3n
um
ber
of s
ides
�20
nu
mbe
r of
sid
es �
20di
amet
er o
f ci
rcle
�24
diam
eter
of
circ
le �
240
3.12
8666
667
3.12
8691
667
5.le
ngt
h o
f on
e si
de �
1.67
546.
len
gth
of
one
side
�2.
6389
nu
mbe
r of
sid
es �
150
nu
mbe
r of
sid
es �
500
diam
eter
of
circ
le �
80di
amet
er o
f ci
rcle
�42
03.
1413
753.
1415
4761
9A
s th
e n
um
ber
of
sid
es in
crea
ses,
the
rati
o g
ets
clo
ser
to t
he
valu
e o
f �
giv
en a
bov
e.
peri
met
er o
f re
gula
r po
lygo
n�
��
��
�di
amet
er o
f ci
rcle
dra
wn
aro
un
d th
e po
lygo
n
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enric
hmen
t
©G
lenc
oe/M
cGra
w-H
ill63
8M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
©G
lenc
oe/M
cGra
w-H
ill63
7M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Pre-
Act
ivit
yC
om
ple
te t
he
Min
i Lab
at
the
top
of
pag
e 49
3 in
yo
ur
text
bo
ok.
Wri
te y
ou
r an
swer
s b
elo
w.
1.W
hat
is
the
mea
sure
men
t of
th
e ba
se a
nd
the
hei
ght?
�1 2�C;
r
2.S
ubs
titu
te t
hes
e va
lues
in
to t
he
form
ula
for
th
e ar
ea o
f a
para
llel
ogra
m.
A�
�1 2�C(r
)
3.R
epla
ce C
wit
h t
he
expr
essi
on f
or t
he
circ
um
fere
nce
of
a ci
rcle
,2�
r.S
impl
ify
the
equ
atio
n a
nd
desc
ribe
wh
at i
t re
pres
ents
.
A�
�1 2�(�
r)(r
);A
��
r2;
the
area
of
a ci
rcle
Rea
din
g t
he
Less
on
4.T
he
form
ula
for
th
e ar
ea o
f a
circ
le u
ses
the
nu
mbe
r �
.How
doe
s th
isaf
fect
th
e va
lue
of t
he
area
of
a ci
rcle
fou
nd
usi
ng
the
form
ula
?S
amp
lean
swer
:Wh
en y
ou
su
bst
itu
te a
val
ue
for
�o
r u
se a
calc
ula
tor
to m
ult
iply
by
�,t
he
resu
lt w
ill b
e o
nly
an
esti
mat
e.
5.If
you
are
giv
en t
he
len
gth
of
the
diam
eter
of
a ci
rcle
,how
can
you
fin
d it
sar
ea?
Sam
ple
an
swer
:D
ivid
e th
e le
ng
th o
f th
e d
iam
eter
by
2,sq
uar
e it
,an
d m
ult
iply
th
e re
sult
by
pi.
Hel
pin
g Y
ou
Rem
emb
er6.
Th
ink
abou
t th
e fo
rmu
las
you
hav
e le
arn
ed t
hat
in
volv
e ci
rcle
s:C
�2�
ror
C�
�d
and
A�
�r2
.To
hel
p yo
u r
emem
ber
the
diff
eren
ce b
etw
een
th
efo
rmu
las
for
circ
um
fere
nce
an
d th
e fo
rmu
la f
or a
rea,
thin
k ab
out
the
diff
eren
ces
in t
he
un
its
use
d fo
r ea
ch m
easu
rem
ent.
Wh
at k
inds
of
un
its
are
use
d fo
r ea
ch?
How
can
th
is h
elp
you
rem
embe
r th
e fo
rmu
la f
or t
he
area
of
a ci
rcle
?S
amp
le a
nsw
er:T
he
un
its
for
the
circ
um
fere
nce
of
a ci
rcle
are
th
e sa
me
as t
he
un
its
for
the
dia
met
er o
r ra
diu
s o
f th
e ci
rcle
.Th
e u
nit
s fo
r th
e ar
ea o
f a
circ
le a
re a
lway
s sq
uar
e u
nit
s,so
th
at m
igh
t h
elp
yo
ure
mem
ber
th
at t
he
form
ula
fo
r th
e ar
ea o
f a
circ
le is
pi t
imes
the
squ
are
of
its
rad
ius.
Read
ing
to L
earn
Mat
hem
atic
sA
rea
of
Cir
cles
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Lesson 11–6
Answers (Lesson 11-6)
© Glencoe/McGraw-Hill A18 Mathematics: Applications and Concepts, Course 2
©G
lenc
oe/M
cGra
w-H
ill64
0M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Prac
tice:
Ski
llsA
rea
of
Co
mp
lex
Fig
ure
sF
ind
th
e ar
ea o
f ea
ch f
igu
re.R
oun
d t
o th
e n
eare
st t
enth
if
nec
essa
ry.
1.12
6.0
cm2
2.90
.3 m
m2
3.55
0 in
24.
59.1
in2
5.97
.8 m
26.
234
yd2
7.16
m2
8.9.
1 ft
2
1.3
ft
1.3
ft
3.5
ft
3.5
ft
3.5
ft
3.5
ft4
m
4 m
2 m2
m
2 m
20 y
d
9 yd
11 y
d
9 yd
4 yd
4 yd
13 m
9 m
7 m
3 in
.4
in.
9 in
.15
in.
5 in
.
10 in
.
30 in
.
15 in
.
7 m
m5
mm
6 m
m
7 cm 7
cm
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Lesson 11–7
©G
lenc
oe/M
cGra
w-H
ill63
9M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Stud
y Gu
ide
and
Inte
rven
tion
Are
a o
f C
om
ple
x F
igu
res
Fin
d t
he
area
of
the
figu
re a
t th
e ri
ght
in s
qu
are
feet
.
Th
e fi
gure
can
be
sepa
rate
d in
to a
rec
tan
gle
and
a tr
apez
oid.
Fin
d th
e ar
ea o
f ea
ch.
Are
a of
Rec
tan
gle
A�
�wA
rea
of a
rec
tang
le
A�
12�
8R
epla
ce �
with
12
and
ww
ith 8
.
A�
96M
ultip
ly.
Are
a of
Tra
pezo
id
A�
�1 2�h(b
1�
b 2)
Are
a of
a t
rape
zoid
A�
�1 2�(4)
(4�
12)
Rep
lace
hw
ith 4
, b 1
with
4,
and
b 2w
ith 1
2.
A�
32M
ultip
ly.
Th
e ar
ea o
f th
e fi
gure
is
96 �
32 o
r 12
8 sq
uar
e fe
et.
Fin
d t
he
area
of
each
fig
ure
.Rou
nd
to
the
nea
rest
ten
th i
f n
eces
sary
.
1.65
cm
22.
25.4
in2
3.80
6.1
mm
218
mm 38
mm
11 m
m
4 in
.5
in.
4 cm
6.5
cm
13 c
m
6 cm
6 cm
12 ft
4 ft
4 ft
12 ft
8 ft
12 ft
4 ft
4 ft
8 ft
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Co
mp
lex
fig
ure
sar
e m
ade
of c
ircle
s, r
ecta
ngle
s, s
quar
es,
and
othe
r tw
o-di
men
sion
al f
igur
es.T
o fin
dth
e ar
ea o
f a
com
plex
fig
ure,
sep
arat
e it
into
fig
ures
who
se a
reas
you
kno
w h
ow t
o fin
d, a
nd t
hen
add
the
area
s.
Answers (Lesson 11-7)
© Glencoe/McGraw-Hill A19 Mathematics: Applications and Concepts, Course 2
An
swer
s
©G
lenc
oe/M
cGra
w-H
ill64
2M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Read
ing
to L
earn
Mat
hem
atic
sA
rea
of
Co
mp
lex
Fig
ure
s
Pre-
Act
ivit
yR
ead
th
e in
tro
du
ctio
n a
t th
e to
p o
f p
age
498
in y
ou
r te
xtb
oo
k.W
rite
yo
ur
answ
ers
bel
ow
.
1.D
escr
ibe
the
shap
e of
th
e ki
tch
en.
rect
ang
le a
nd
sem
icir
cle
2.H
ow c
ould
you
det
erm
ine
the
area
of
the
kitc
hen
?S
amp
le a
nsw
er:
Fin
d t
he
area
of
the
rect
ang
le a
nd
th
e ar
ea o
f th
e se
mic
ircl
e,th
en a
dd
.
3.H
ow c
ould
you
det
erm
ine
the
tota
l sq
uar
e fo
otag
e of
a h
ouse
wit
h r
oom
s sh
aped
like
th
ese?
Sam
ple
an
swer
:F
ind
th
e ar
ea o
f ea
ch r
oo
m,t
hen
ad
d.
Rea
din
g t
he
Less
on
4.L
ook
up
the
term
foo
tage
in a
dic
tion
ary.
Wri
te t
he
mea
nin
g th
at m
atch
esth
e w
ay t
he
term
is
use
d in
th
is l
esso
n.
Sam
ple
an
swer
:le
ng
th o
r q
uan
tity
exp
ress
ed in
fee
t5.
Wh
at d
o yo
u t
hin
k th
e te
rm s
quar
e fo
otag
em
ean
s?S
amp
le a
nsw
er:
area
in s
qu
are
feet
6.W
hic
h w
ord
of t
he
com
pou
nd
squ
are
foot
age
indi
cate
s ar
ea?
Exp
lain
.S
amp
le a
nsw
er:
squ
are,
bec
ause
are
a is
mea
sure
d in
sq
uar
e u
nit
s7.
Loo
k u
p th
e te
rm t
wo-
dim
ensi
onal
in a
dic
tion
ary.
Sam
ple
an
swer
:h
avin
g t
wo
dim
ensi
on
s,es
pec
ially
len
gth
an
d w
idth
;p
lan
ar;
flat
8.N
ame
two
dim
ensi
ons
of e
ach
of
the
foll
owin
g fi
gure
s.
a.re
ctan
gle
b.
para
llel
ogra
mc.
tria
ngl
ele
ng
th a
nd
wid
thb
ase
and
hei
gh
tb
ase
and
hei
gh
t
9.R
efer
to
the
figu
re i
n E
xam
ple
2 on
pag
e 49
9.H
ow d
o yo
u k
now
th
at t
he
base
and
hei
ght
of t
he
tria
ngl
e ar
e ea
ch 4
in
ches
lon
g?S
amp
le a
nsw
er:T
he
len
gth
of
the
rect
ang
le is
10
inch
es,a
nd
th
e si
de
of
the
rect
ang
lew
her
e th
e tr
ian
gle
mee
ts t
he
rect
ang
le is
6 in
ches
lon
g p
lus
the
len
gth
of
the
sid
e o
f th
e tr
ian
gle
.So
,yo
u c
an s
ub
trac
t 6
fro
m 1
0 to
fin
d t
he
len
gth
of
the
sid
e o
f th
e tr
ian
gle
.
Hel
pin
g Y
ou
Rem
emb
er10
.L
ook
in a
dic
tion
ary
for
the
mea
nin
gs o
f th
e w
ord
com
plex
wh
en u
sed
as
an a
djec
tive
.Wri
te t
he
mea
nin
g of
th
e w
ord
as i
t is
use
d in
th
is l
esso
n.
Wh
y ca
n t
he
figu
res
in E
xam
ples
1 a
nd
2 be
con
side
red
com
plex
fig
ure
s?S
amp
lean
swer
:Th
e w
ord
co
mp
lex
mea
ns
“mad
e u
p o
f tw
o o
r m
ore
par
ts.”
Th
efi
gu
re in
Exa
mp
le 1
can
be
sep
arat
ed in
to a
rec
tan
gle
an
d a
sem
icir
cle;
the
fig
ure
in E
xam
ple
2 c
an b
e se
par
ated
into
a r
ecta
ng
le a
nd
a t
rian
gle
.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
©G
lenc
oe/M
cGra
w-H
ill64
1M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Prac
tice:
Wor
d Pr
oble
ms
Are
a o
f C
om
ple
x F
igu
res
AR
CH
ITEC
TUR
EF
or E
xerc
ises
1–6
use
Jac
o’s
pre
lim
inar
y d
esig
n o
f h
is v
acat
ion
hou
se
at t
he
righ
t.R
oun
d t
o th
e n
eare
st t
enth
if
nec
essa
ry.
8 ft
4 ft 4 ft
4 ft
8 ft
4 ft
4 ft
4 ft
8 ft
8 ft
4 ft
4 ft
2 ft
4 ft
12 ft
4 ft
12 ft
16 ft
16 ft
12 ft
16 ft
16 ft4 ft
4 ft
bedr
oom
1ki
tche
nbe
droo
m2
b a t h r o o m
livin
gro
omde
n
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Lesson 11–7
1.W
hat
typ
e of
fig
ure
is
bedr
oom
1?
Fin
dth
e ar
ea o
f be
droo
m 1
.tr
apez
oid
;21
6 ft
2
2.W
hat
is
the
area
of
the
bedr
oom
2?
Wh
at f
igu
res
did
you
use
to
fin
d th
ear
ea?
224
ft2 ;
squ
are
and
rect
ang
le
3.W
hat
is
the
area
of
the
bath
room
?W
hat
are
th
e di
men
sion
s of
th
e fi
gure
syo
u u
sed
to f
ind
this
are
a?96
ft2
;8
ft b
y 4
ft r
ecta
ng
le a
nd
16
ft b
y4
ft r
ecta
ng
le
4.W
hat
is
the
area
of
the
livi
ng
room
?H
ow m
any
figu
res
did
you
use
to
fin
dth
is a
rea?
256
ft2 ;
Sam
ple
answ
er:
3
5.W
hat
is
the
area
of
the
den
? W
hat
wou
ld t
he
area
of
the
den
be
if t
he
sem
icir
cula
r w
indo
w w
ere
rem
oved
an
dre
plac
ed w
ith
a f
lat
win
dow
?19
8.3
ft2 ;
192
ft2
6.W
hat
is
the
area
of
the
kitc
hen
? If
Jac
oad
ds a
rec
tan
gula
r co
okin
g is
lan
d in
the
mid
dle
of t
he
kitc
hen
wit
hdi
men
sion
s 6
feet
by
4 fe
et,h
ow m
any
squ
are
feet
of
wal
kin
g sp
ace
wil
l be
left
?35
2 ft
2 ;32
8 ft
2
Answers (Lesson 11-7)
© Glencoe/McGraw-Hill A20 Mathematics: Applications and Concepts, Course 2
©G
lenc
oe/M
cGra
w-H
ill64
4M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Stud
y Gu
ide
and
Inte
rven
tion
Are
a M
od
els
and
Pro
bab
ility
A r
and
omly
-dro
pp
ed c
oun
ter
fall
s so
mew
her
e in
th
e sq
uar
es.F
ind
th
e p
rob
abil
ity
that
it
fall
s on
th
e sh
aded
sq
uar
es.
prob
abil
ity
�
�
Are
a of
Sh
aded
Squ
ares
Are
a of
All
Squ
ares
A�
�r2
Are
a of
a c
ircle
A�
�1 2�bh
Are
a of
a t
riang
le
A�
��
12r
�1
A�
�1 2�(5)
(6)
b�
5 an
d h
�6
A�
3.1
Sim
plify
.A
�15
Sim
plify
.
So,
the
prob
abil
ity
of a
cou
nte
r fa
llin
g in
th
e sh
aded
squ
ares
is
abou
t �3 1. 51 �
orab
out
20.7
%.
A r
and
omly
-dro
pp
ed c
oun
ter
fall
s in
th
e sq
uar
es.F
ind
th
ep
rob
abil
ity
that
it
fall
s in
th
e sh
aded
sq
uar
es.W
rite
as
a p
erce
nt.
Rou
nd
to
the
nea
rest
ten
th i
f n
eces
sary
.
1.10
%2.
22.4
%3.
93.3
%
4.5.
6.
25.8
%30
.4%
27.0
%
area
of
shad
ed s
quar
es�
��
area
of
all
squ
ares
nu
mbe
r of
way
s to
lan
d in
sh
aded
squ
ares
��
��
�n
um
ber
of w
ays
to l
and
on s
quar
es
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
You
can
rela
te p
roba
bilit
y to
the
are
a of
geo
met
ric s
hape
s.
©G
lenc
oe/M
cGra
w-H
ill64
3M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Exte
nd
ing
th
e Py
thag
ore
an T
heo
rem
Th
e P
yth
agor
ean
Th
eore
m s
ays
that
th
e su
m o
f th
e ar
eas
of t
he
two
smal
ler
squ
ares
is
equ
al t
o th
e ar
ea o
f th
e la
rges
t sq
uar
e.S
how
th
at t
he
Pyt
hag
orea
n T
heo
rem
can
be
exte
nde
d to
in
clu
deot
her
sh
apes
on
th
e si
des
of a
tri
angl
e.T
o do
so,
fin
d th
e ar
eas
ofth
e tw
o sm
alle
r sh
apes
.Th
en,c
hec
k th
at t
hei
r su
m e
qual
s th
ear
ea o
f th
e la
rges
t sh
ape.
1.ar
ea o
f sm
alle
st s
hap
e:3.
5 in
22.
area
of
smal
lest
sh
ape:
2.25
in2
area
of
mid
dle
shap
e:6.
3 in
2ar
ea o
f m
iddl
e sh
ape:
4 in
2
area
of
larg
est
shap
e:9.
8 in
2ar
ea o
f la
rges
t sh
ape:
6.25
in2
3.ar
ea o
f sm
alle
st s
hap
e:4.
5 in
24.
area
of
smal
lest
sh
ape:
3.9
in2
area
of
mid
dle
shap
e:8
in2
area
of
mid
dle
shap
e:6.
9 in
2
area
of
larg
est
shap
e:12
.5 in
2ar
ea o
f la
rges
t sh
ape:
10.8
in2
3 in
.
3 in
.
3 in
.
5 in
.
5 in
.
5 in
.
4 in
.
4 in
.4
in.
3 in
.
3 in
.
5 in
.5
in.
4 in
.
4 in
.
1.5 in.
3 in
.
5 in
. 4 in
.
2.5
in.
2 in
.
5 in
.
4 in
.
3 in
.
55
44
33
Enric
hmen
tN
AM
E__
____
____
____
____
____
____
____
____
____
__D
ATE
___
____
____
___
PE
RIO
D
____
_
Lesson 11–7
Answers (Lessons 11-7 and 11-8)
© Glencoe/McGraw-Hill A21 Mathematics: Applications and Concepts, Course 2
An
swer
s
©G
lenc
oe/M
cGra
w-H
ill64
6M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Prac
tice:
Wor
d Pr
oble
ms
Are
a M
od
els
and
Pro
bab
ility
GA
MES
Eac
h f
igu
re r
epre
sen
ts a
sq
uar
e d
artb
oard
.If
it i
s eq
ual
lyli
kel
y th
at a
th
row
n d
art
wil
l la
nd
an
ywh
ere
on t
he
dar
tboa
rd,f
ind
the
pro
bab
ilit
y th
at i
t la
nd
s in
th
e sh
aded
reg
ion
.Rou
nd
to
the
nea
rest
ten
th.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
1.
26.2
%
2.
17.5
%
3.
33.3
%
4.
9.6%
5 cm
30 c
m
10 c
m
2 in
.
12 in
.
2 in
.
4 in
.
8 in
.
12 in
.
4 in
.11
.3 in
.
16 in
.Lesson 11–8
©G
lenc
oe/M
cGra
w-H
ill64
5M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Prac
tice:
Ski
llsA
rea
Mo
del
s an
d P
rob
abili
tyA
ran
dom
ly-d
rop
ped
cou
nte
r fa
lls
in t
he
squ
ares
.Fin
d t
he
pro
bab
ilit
y th
at i
t fa
lls
in t
he
shad
ed s
qu
ares
.Wri
te a
s a
per
cen
t.R
oun
d t
o th
e n
eare
st t
enth
if
nec
essa
ry.
1.16
.7%
2.87
.2%
3.28
.6%
4.21
.4%
5.15
.2%
6.37
.3%
7.11
.1%
8.19
.6%
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Answers (Lesson 11-8)
© Glencoe/McGraw-Hill A22 Mathematics: Applications and Concepts, Course 2
Are
a Fo
rmu
las
for
Reg
ula
r Po
lyg
on
sR
ecal
l th
at t
he
side
s of
a r
egu
lar
poly
gon
are
all
th
e sa
me
len
gth
.Her
e ar
eso
me
area
for
mu
las
for
fou
r of
th
e re
gula
r po
lygo
ns.
Th
e va
riab
le s
stan
dsfo
r th
e le
ngt
h o
f on
e si
de.
tria
ngl
ep
enta
gon
hex
agon
octa
gon
A�
�s 42 ��
3�A
��s 42 �
�25
�1
�0�
5��
A�
�3 2s2 ��
3�A
�2s
2 (�
2��
1)
Fin
d t
he
area
of
each
pol
ygon
wit
h t
he
sid
e of
giv
en l
engt
h.U
se a
calc
ula
tor
and
rou
nd
eac
h a
nsw
er t
o th
e n
eare
st t
enth
.
1. 2. 3. 4. Now
use
th
e ta
ble
ab
ove
to f
ind
th
e ar
ea o
f ea
ch s
had
ed r
egio
n b
elow
.U
nle
ss o
ther
wis
e sp
ecif
ied
,eac
h s
egm
ent
is 1
cen
tim
eter
lon
g.
5.6.
7.
3.8
cm2
1.3
cm2
1.8
cm2
8.9.
10.
5.6
cm2
5.4
cm2
6.2
cm2
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enric
hmen
t
©G
lenc
oe/M
cGra
w-H
ill64
8M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Len
gth
of
a S
ide
Tri
angl
eP
enta
gon
Hex
agon
Oct
agon
1 cm
0.4
cm2
1.7
cm2
2.6
cm2
4.8
cm2
2 cm
1.7
cm2
6.9
cm2
10.4
cm
219
.3 c
m2
3 cm
3.9
cm2
15.5
cm
223
.4 c
m2
43.5
cm
2
4 cm
6.9
cm2
27.5
cm
241
.6 c
m2
77.3
cm
2
2 cm
2 cm
3 cm
©G
lenc
oe/M
cGra
w-H
ill64
7M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 2
Read
ing
to L
earn
Mat
hem
atic
sA
rea
Mo
del
s an
d P
rob
abili
ty
Pre-
Act
ivit
yC
om
ple
te t
he
Min
i Lab
at
the
top
of
pag
e 50
1 in
yo
ur
text
bo
ok.
Wri
te y
ou
r an
swer
s b
elo
w.
1.D
o ce
rtai
n p
rodu
cts
occu
r m
ore
ofte
n?
See
stu
den
ts’w
ork
.
2.M
ake
and
com
plet
e th
e ta
ble
belo
w t
o fi
nd
all
the
poss
ible
ou
tcom
es.
Rea
din
g t
he
Less
on
3.H
ow c
an y
ou u
se t
he
grid
fol
low
ing
the
intr
odu
ctio
n i
n y
our
text
book
to
dete
rmin
e th
at t
he
prob
abil
ity
of r
olli
ng
two
nu
mbe
rs w
hos
e pr
odu
ct i
s 6
or 1
2 is
�2 9�?S
amp
le a
nsw
er:T
he
nu
mb
ers
6 an
d 1
2 ap
pea
r in
8o
f th
e 36
sq
uar
es o
f th
e g
rid
,so
th
ey m
ake
up
�2 9�o
f th
e ar
eao
f th
e g
rid
.
4.T
he
form
ula
for
pro
babi
lity
is �de
tos tir ae ld ara er aea
�.H
ow d
oes
this
les
son
sim
plif
y
the
expr
essi
on f
or p
roba
bili
ty?
Sam
ple
an
swer
:In
stea
d o
f h
avin
gto
co
un
t ev
ery
squ
are
un
it f
or
each
ou
tco
me,
you
can
use
the
nu
mb
ers
of
squ
are
un
its
for
each
ou
tco
me,
that
is,t
he
area
s.
Hel
pin
g Y
ou
Rem
emb
er5.
Fin
d th
e di
men
sion
s of
a t
arge
t fo
r da
rts
or f
or a
bow
an
d ar
row
.Dra
w a
mod
el t
hat
sh
ows
the
mea
sure
men
ts.T
hen
sh
ow t
he
prob
abil
ity
of h
itti
ng
the
area
th
at s
core
s th
e m
ost
poin
ts p
er h
it.
See
stu
den
ts’w
ork
.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Lesson 11–8
�1
23
45
6
11
23
45
6
22
46
810
12
33
69
1215
18
44
812
1620
24
55
1015
2025
30
66
1218
2430
36
Answers (Lesson 11-8)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13. C
I
B
F
C
G
D
G
B
H
A
H
D
�11
I
A
I
B
H
C
H
A
I
A
H
A
H
B
H
C
I
A
I
B
Chapter 11 Assessment Answer KeyForm 1 Form 2APage 649 Page 650 Page 651
(continued on the next page)
© Glencoe/McGraw-Hill A23 Mathematics: Applications and Concepts, Course 2
An
swer
s
14.
15.
16.
17.
18.
19.
20.
B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: �27
I
C
F
B
I
D
I
D
G
D
I
A
G
B
H
A
I
A
I
B
�23
F
B
H
A
I
C
F
Chapter 11 Assessment Answer KeyForm 2A (continued) Form 2BPage 652 Page 653 Page 654
© Glencoe/McGraw-Hill A24 Mathematics: Applications and Concepts, Course 2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: 14 in.
907.9 in2
113.1 cm2
288 mi2
476.7 m2
108 mm2
32 ft2
4.7 m
40 ft
8.5 cm
21.3
9.5
7
5
37
12
1,600
81
19
12 ft
30%
Chapter 11 Assessment Answer KeyForm 2CPage 655 Page 656
© Glencoe/McGraw-Hill A25 Mathematics: Applications and Concepts, Course 2
An
swer
s
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: 12 ft
615.8 in2
38.5 ft2
576 cm2
57.1 in2
500 mm2
36 m2
7.8 cm
6.2 ft
75 m
17.9
8.9
9
6
33
11
900
16
83
14 mi
20%
Chapter 11 Assessment Answer KeyForm 2DPage 657 Page 658
© Glencoe/McGraw-Hill A26 Mathematics: Applications and Concepts, Course 2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: 18.5 in.
1,170.2 m2
7,854.0 ft2
900 cm2
138.4 ft2
360 m2
160 cm2
10.0 in.
14.2 yd
48 m
30.5
8.2
12
9
16
21
1,024
361
259
24 ft
16.7%
Chapter 11 Assessment Answer KeyForm 3Page 659 Page 660
© Glencoe/McGraw-Hill A27 Mathematics: Applications and Concepts, Course 2
An
swer
s
© Glencoe/McGraw-Hill A28 Mathematics: Applications and Concepts, Course 2
Level Specific Criteria
4 The student demonstrates a thorough understanding of the mathematicsconcepts and/or procedures embodied in the task. The student hasresponded correctly to the task, used mathematically sound procedures,and provided clear and complete explanations and interpretations. Theresponse may contain minor flaws that do not detract from thedemonstration of a thorough understanding.
3 The student demonstrates an understanding of the mathematics conceptsand/or procedures embodied in the task. The student’s response to thetask is essentially correct with the mathematical procedures used and theexplanations and interpretations provided demonstrating an essential butless than thorough understanding. The response may contain minor errorsthat reflect inattentive execution of the mathematical procedures orindications of some misunderstanding of the underlying mathematicsconcepts and/or procedures.
2 The student has demonstrated only a partial understanding of themathematics concepts and/or procedures embodied in the task. Althoughthe student may have used the correct approach to obtaining a solution ormay have provided a correct solution, the student’s work lacks an essentialunderstanding of the underlying mathematical concepts. The responsecontains errors related to misunderstanding important aspects of the task,misuse of mathematical procedures, or faulty interpretations of results.
1 The student has demonstrated a very limited understanding of themathematics concepts and/or procedures embodied in the task. Thestudent’s response to the task is incomplete and exhibits many flaws.Although the student has addressed some of the conditions of the task, thestudent reached an inadequate conclusion and/or provided reasoning thatwas faulty or incomplete. The response exhibits many errors or may beincomplete.
0 The student has provided a completely incorrect solution oruninterpretable response, or no response at all.
Chapter 11 Assessment Answer KeyPage 661, Extended Response Assessment
Scoring Rubric
An
swer
s
© Glencoe/McGraw-Hill A29 Mathematics: Applications and Concepts, Course 2
Chapter 11 Assessment Answer Key Page 661, Extended Response Assessment
Answer Key
1. a. The square root of a number is one ofits two equal factors.
b.
�17� � 4
c. In a right triangle, the square of thelength of the hypotenuse is equal tothe sum of the squares of the lengthsof the legs.
d.
e. No, �482 �� 362� equals 60, not 62.
f. Use the Pythagorean Theorem.
a2 � b2 � c2
302 � 362 � c2
900 � 1,296 � c2 Find the squares.
2,196 � c2 Add.
�2,196� � c Find the square root.
46.9 � c
2. Find the area of the trapezoidal parkand subtract the areas of the circularfountain and triangular botanicalgarden. Multiply this area by the costper square foot.
Area � �12� � 175(300 � 350) � �202
� �12� � 145 � 125 � 46,556
Mrs. Cobel’s bid:46,556 � $1.50 � $69,834
4
4
4 � 4 17�
�
In addition to the scoring rubric found on page A28, the following sample answersmay be used as guidance in evaluating extended response assessment items.
1. false; square
2. true
3. false; hypotenuse
4. false; angle
5. false; hypotenuse
6. true
7. false; radical
8. true
9. false; complexfigures
10. true
11. a theorem that saysthat in a righttriangle, the squareof the length of thehypotenuse equalsthe sum of thesquares of thelengths of the legs
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Quiz (Lessons 11-3 and 11-4)
Page 663
1.
2.
3.
4.
5.
1.
2.
3.
4.
5.
Quiz (Lessons 11-7 and 11-8)
Page 664
1.
2.
3.
4.
5. 13.3%
20%
30%
25 in2
76.8 ft2
10.2 cm2
50.3 in2
792 ft2
1,950 mm2
3,840 m2
663 ft2
38.3 m2
21 mm
7.9 cm
50 ft
1715
12826196
1,2961,849529
Chapter 11 Assessment Answer KeyVocabulary Test/Review Quiz (Lessons 11-1 and 11-2) Quiz (Lessons 11-5 and 11-6)
Page 662 Page 663 Page 664
© Glencoe/McGraw-Hill A30 Mathematics: Applications and Concepts, Course 2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13. 7.1 in2
31.5 mm2
5.24 m
11
y
xO
R'
P'
PQ'
Q
R
P�(�2, 0); Q�(0, 3);R�(3, �2);
No; 144° does notdivide evenly into 360°.
the chance of nosnow; 55%
250%
�56090
�
4
29�14
�
�12
�
�18e
3.6 m
20.2 m5 cm
2017
1815
25681
H
B
F
D
F
C
Chapter 11 Assessment Answer KeyMid-Chapter Test Cumulative ReviewPage 665 Page 666
© Glencoe/McGraw-Hill A31 Mathematics: Applications and Concepts, Course 2
An
swer
s
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13. 14.
15.
16.
17. a.
b. 17.0 ft
pole21 ft
board27 ft
x ft
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
01 0
120 outcomes
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
63
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
55 .1
�14, �10, �8,�3, 0, 11
DCBA
IHGF
DCBA
IHGF
DCBA
IHGF
DCBA
IHGF
DCBA
IHGF
DCBA
Chapter 11 Assessment Answer KeyStandardized Test PracticePage 667 Page 668
© Glencoe/McGraw-Hill A32 Mathematics: Applications and Concepts, Course 2