Interim 4th review

Find the area of the triangle.

Check It Out: Example 1B

A = 12

bh Write the formula.

A = 54

The area is 54 in2.

A = 12

(108) Multiply.

24 ft

4 ft12

A = 12

(4 • 24)12

Substitute 4 for b and 24 for h.

12

Find the area of the trapezoid.

Additional Example 3: Finding the Area of a Trapezoid

A = 12

h(b1 + b2) Use the formula.

A = 53

The area is 53 yd2.

Multiply.

A =12

· 4(26 )12

Substitute 4 for h, 14 for b1, and 12 for b2.

12

A = 12

· 4(14 + 12 )12

Lesson Quiz

Find the area of each triangle.

1.

3.

84 mi22.

4.

Find the area of each trapezoid.

39.9 cm2

22.5 m2 113 in23 4

Additional Example 1A: Finding Areas of Composite Figures

Find the area of the polygon.

Think: Break the polygon apart into rectangles.

Find the area of each rectangle.

1.7 cm

4.9 cm 1.3 cm

2.1 cm

Additional Example 1A Continued

A = lw A = lw

A = 4.9 • 1.7 A = 2.1 • 1.3Write the formula for the area of a rectangle.A = 8.33 A = 2.73

8.33 + 2.73 = 11.06 Add to find the total area.

The area of the polygon is 11.06 cm2.

1.7 cm

4.9 cm

1.3 cm

2.1 cm

Think: Break the figure apart into a rectangle and a triangle.

Find the area of each polygon.

Additional Example 1B: Finding Areas of Composite Figures

Find the area of the polygon.

Additional Example 1B Continued

A = lw

A = 28 • 24

A = 672 A = 168

672 + 168 = 840 Add to find the total area of the polygon.

The area of the polygon is 840 ft2.

A = bh12__

A = • 28 • 1212__

Lesson Quiz

1. Find the area of the figure shown.

220 units2

2. Phillip designed a countertop. Use the coordinate grid to find its area.

30 units2

Lesson Quiz

Find how the perimeter and area of the triangle change when its dimensions change.

The perimeter is multiplied by 2, and the area is multiplied by 4; perimeter = 24, area = 24; perimeter = 48, area = 96.

Insert Lesson Title Here

Course 1

10-4 Comparing Perimeter and Area

Additional Example 1A: Estimating the Area of a Circle

Estimate the area of the circle. Use 3 to approximate pi.

A ≈ 3 • 202

A ≈ 1200 m2

Course 1

10-5 Area of Circles

19.7 m

A = r2 Write the formula for area.

Replace with 3 and r with 20.

A ≈ 3 • 400Use the order of operations.

Multiply.

Additional Example 1B: Estimating the Area of a Circle

Estimate the area of the circle. Use 3 to approximate pi.

r = 28 ÷ 2

A ≈ 3 • 142

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28 m

A = r2 Write the formula for area.

Replace with 3 and r with 14.

r = 14

Use the order of operations.

Divide.

r = d ÷ 2 The length of the radius is half the length of the diameter.

A ≈ 3 • 196

A ≈ 588 m2 Multiply.

Additional Example 2A: Using the Formula for the Area of a Circle

Find the area of the circle. Use for pi.

Write the formula to find the area.A = r2

r = d ÷ 2r = 8 ÷ 2 = 4

The length of the diameter is twice the length of the radius.

Replace with and r with 4.22

7 __

A • 16 22

7 __ Use the order of operations.

A 50.29 ft2 Divide.

22 7

A • (4)222

7

8 ft

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352

7

Lesson Quiz: Part I

Estimate the area of each circle.

1. 2.


3 km

27 km2 1200 yd2

38 yd

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3. 4.


4.53 cm2 1.54 m2

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Lesson Quiz: Part II

Find the area of each circle. Use for pi.22 7

2.4 cm 0.7 m

5. A coater has a diameter of 6 inches. Find the area of the largest cup the coaster can hold. Use 3.14 for pi.28.26 in2

A polyhedron is a three-dimensional object, or solid figure, with flat surfaces, called faces, that are polygons.

When two faces of a three-dimensional figure share a side, they form an edge. On a three-dimensional figure, a point at which three or more edges meet is a vertex (plural: vertices).

Course 1

10-6 Three-Dimensional Figures

Additional Example 1: Identifying Faces, Edges, and Vertices

Identify the number of faces, edges, and vertices on each three-dimensional figure.

A.

B.

5 faces

8 edges

5 vertices

7 faces

15 edges

10 vertices

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A prism is a polyhedron with two congruent, parallel bases, and other faces that are all parallelograms. A prism is named for the shape of its bases. A cylinder also has two congruent, parallel bases, but bases of a cylinder are circular. A cylinder is not a polyhedron because not every surface is a polygon.

Course 1


A pyramid has one polygon shaped base, and the other faces are triangles that come to a point. A pyramid is named for the shape of its base. A cone has a circular base and a curved surface that comes to a point. A cones is not a polyhedron because not every surface is a polygon.

Course 1


Lesson Quiz

1. Identify the number of faces, edges, and vertices in the figure shown.

Identify the figure described

2. two congruent circular faces connected by a

curved surface

3. one flat circular face and a curved lateral

surface that comes to a point

cylinder

8 faces, 18 edges, and 12 vertices


cone

Course 1


Additional Example 1: Finding the Volume of a Rectangular Prism

Find the volume of the rectangular prism.

V = lwh Write the formula.

V = 26 • 11 • 13 l = 26; w = 11; h = 13

Multiply.V = 3,718 in3

13 in.

26 in.11 in.

Course 1

10-7 Volume of Prisms

Additional Example 2A: Finding the Volume of a Triangular Prism

Find the volume of each triangular prism.

V = Bh Write the formula.

V = ( • 3.9 • 1.3) • 412__ B = • 3.9 • 1.3; h = 4.1

2__

Multiply.V = 10.14 m3

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Lesson Quiz

Find the volume of each figure.

1. rectangular prism with length 20 cm, width

15 cm, and height 12 cm

2. triangular prism with a height of 12 cm and a

triangular base with base length 7.3 cm and

height 3.5 cm

3. Find the volume of the figure shown.


3,600 cm3

153.3 cm3

38.13 cm3

Course 1


Additional Example 1A: Finding the Volume of a Cylinder

Find the volume V of the cylinder to the nearest cubic unit.

Write the formula.

Replace with 3.14, r with 4, and h with 7.Multiply.V 351.68

V = r2h

V 3.14 42 7

The volume is about 352 ft3.

Course 1

10-8 Volume of Cylinders

Check It Out: Example 1B

Multiply.V 301.44

8 cm ÷ 2 = 4 cm

The volume is about 301 cm3.

Find the radius.

8 cm

6 cm

Write the formula.

Replace with 3.14, r with 4, and h with 16.

V = r2h

V 3.14 42 6

Course 1


Lesson Quiz: Part I

Find the volume of each cylinder to the nearest cubic unit. Use 3.14 for .


cylinder b

1,560.14 ft3

193 ft3

1,017 ft3

1,181.64 ft3

Course 1


1. radius = 9 ft, height = 4 ft

2. radius = 3.2 ft, height = 6 ft

3. Which cylinder has a greater volume?

a. radius 5.6 ft and height 12 ft

b. radius 9.1 ft and height 6 ft



about 396 in2

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4. Jeff’s drum kit has two small drums. The first drum has a radius of 3 in. and a height of 14 in. The other drum has a radius of 4 in. and a height of 12 in. Estimate the volume of each cylinder to the nearest cubic inch.

a. First drum

b. Second drum about 603 in2

Additional Example 2: Finding the Surface Area of a Pyramid

Find the surface area S of the pyramid.S = area of square + 4 (area of

triangular face)

S = 49 + 4 28

S = 49 + 112

Substitute.

S = s2 + 4 ( bh) 12__

S = 72 + 4 ( 7 8)12__

S = 161The surface area is 161 ft2.

Course 1

10-9 Surface Area

Additional Example 3: Finding the Surface Area of a Cylinder

Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth.

S = area of lateral surface + 2 (area of each base)

Substitute.S = h (2r) + 2 (r2)

S = 7 (2 4) + 2 ( 42)

ft

Course 1

10-9 Surface Area

Lesson Quiz

Find the surface area of each figure. Use 3.14 for .

1. rectangular prism with base length 6 ft, width

5 ft, and height 7 ft

2. cylinder with radius 3 ft and height 7 ft

3. Find the surface area of the figure shown.


Course 1

10-9 Surface Area

214 ft2

188.4 ft2

208 ft2

You can use the information in the table below to convert one customary unit to another.

Course 1

9-3 Converting Customary Units

When you convert units of measure to another, you can multiply or divide by a conversion factor.

Convert 3 quarts to cups.

Additional Example 2: Converting Units of Measure by Using Proportions

Convert quarts to cups.

1x = 12

1 • x = 4 • 3

3 quarts = 12 cups.

1 quart is 4 cups. Write a proportion. Use a variable for the value you are trying to find.The cross products are equal.Divide both sides by 1 to undo the multiplication.

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3 qt = cups

1 qt 4 c

3 qt x

=

x = 12

Convert 144 cups to gallons.

Check It Out: Example 2

Convert cups to gallons.

16x = 144

16 • x = 1 • 144

144 cups = 9 gallons.

1 gallon is 16 cups. Write a proportion. Use a variable for the value you are trying to find.

The cross products are equal.

Divide both sides by 16 to undo multiplication.

Course 1


144 cups = gallons.

1 gal 16 c

x 144 c=

x = 9

Lesson Quiz

1. Convert 5 yards to inches.

2. Convert 16 tons to pounds.

3. Convert 11 quarts to cups.

4. A project requires 288 inches of tape. How

many yards is this?

32,000 pounds

180 inches


44 cups

8 yards

Course 1


Lesson Quiz

Convert.

1. A book is 24 cm long. 24 cm = ____ mm

2. The chain has a mass of 16 g. 16 g = _____ mg

3. The volume of the liquid was 12,000 mL.

12,000 mL = ____ L

4. Frank’s paper airplane glided 78.9 m. Sarah’s

plane glided 85 m. How many more centimeters

did Sarah’s plane glide?

16,000

240


12

610 cm

Course 1


Additional Example 1: Finding the Perimeter of a Polygon

Find the perimeter of the figure.

2.8 + 3.6 + 3.5 + 3 + 4.3

Add all the side lengths.

The perimeter is 17.2 in.

Course 1

9-7 Perimeter

Lesson Quiz: Part I

Find each perimeter.

1. 2.

3. What is the perimeter of a polygon with side

lengths of 15 cm, 18 cm, 21 cm, 32 cm, and 26

cm?

9 cm

4 ft


112 cm

56__

Course 1

9-7 Perimeter

Lesson Quiz: Part I

Find each perimeter.

1. 2.

3. What is the perimeter of a polygon with side

lengths of 15 cm, 18 cm, 21 cm, 32 cm, and 26

cm?

9 cm

4 ft


112 cm

56__

Course 1

9-7 Perimeter

Warm Up

Write impossible, unlikely, as likely as not, likely, or certain to describe each event.

1. A particular person’s birthday falls on the first of a month.

2. You roll an odd number on a fair number cube.

3. There is a 0.14 probability of picking the winning ticket. Write this as a fraction and as a percent.

unlikely

as likely as not

Course 1

12-2 Experimental Probability

, 14%750__

Performing an experiment is one way to estimate the probability of an event. If an experiment is repeated many times, the experimental probability of an event is the ratio of the number of times the event occurs to the total number of times the experiment is performed.

Course 1


Check It Out: Example 2

For one month, Ms. Simons recorded the time at which her bus arrived. She organized her results in a frequency table.

Time 4:31-4:40 4:41-4:50 4:51-5:00

Frequency 4 8 12

Course 1


Check It Out: Example 2A

=4 + 8

24_____

=12

24___ =

1

2__

Before 4:51 includes 4:31-4:40 and 4:41-4:50.

P(before 4:51) number of times the event occurstotal number of trials

___________________________

Find the experimental probability that the bus will arrive before 4:51.

Course 1



2. Find the experimental probability that the spinner will land on blue.

3. Find the experimental probability that the spinner will land on red.

4. Based on the experiment, what is the probability that the spinner will land on red or blue?


2

9__

4

9__

Sandra spun the spinner above several times and recorded the results in the table.

Course 1


2

3__

An experiment with equally likely outcomes is said to be fair. You can usually assume that experiments involving items such as coins and number cubes are fair.

Course 1

12-6 Theoretical Probability

When you combine all the ways that an event can NOT happen, you have the complement of the event.

Course 1


Lesson Quiz

Use the spinner shown for problems 1-3.

1. P(2)

2. P(odd number)

3. P(factor of 6)

4. Suppose there is a 2% chance of spinning the

winning number at a carnival game. What is

the probability of not winning?


98%

2

7__

4

7__

4

7__

Course 1


Education

Interim 4th review