Geometry Name: ___________________ Composite Area I Worksheet Period: ____ Date: _________ 4. Find the areas contained in the shapes.

7. Find the areas contained in the shapes.

9. Find the shaded area.

11. Delta's backyard is rectangular. Its dimensions are 15.0 m by 10.0 m. Delta's family is making a garden from the patio doors to the corners at the back of the yard. The patio doors are 2.0 m wide. Determine the area of the garden. Show your work.

Worksheet – Composite Areas II 7. Find the area contained in an isosceles right triangle with semi circles attached to each side.

9. Calculate the non shaded area:

3 cm 6 cm

4 cm

7 cm

2 mm 2 mm

4 mm

4 cm

24 cm

8 cm 8 cm

26

15

10. Calculate the non shaded area:

13. Calculate the shaded area:

17. Find the value of h. (Hint: Find the area using 10 as the base; then use that area to work backwards to find the h with 8 as the base.)

18. Sonja wants to place a decorative brick edging around a flower garden that is in the shape of a rhombus. One diagonal is 30 feet long, and the area is 600 square feet. How many bricks must she purchase if each brick is one foot long?

19. Graph the lines and find the area of the triangle enclosed by the lines. y = 7 x = -3 y = 2x – 1

20. Find the area of quadrilateral QRST with vertices Q(-2, -1), R(-2, 2), S(2, 3), and T(1, -1).

15. Calculate the shaded area:

8 in

12

28

30°

8 h 7

10

2 ft

12 ft

27 ft

8 ft 4 ft

10-3 and 10-5: Answers to Pg 548 # 2-26 (every 4th question), 15-17 all, 32-33; Pg 561 # 2-26 (every 4th question), 20, 23, 33, 36.

Pg 5482. m∠4=90°, m∠5=45°, m∠6=45°6. 12,080 in2

10. 486√3 = 841.8 ft214. 72 cm2

18. 12√3 in2

22. (a) 30°. (b) 75°26. m∠1=36°, m∠2=18°, m∠3=72°15. 384√3 in2

16. 162√3 m2

17. 75√3 m2

32. 24√3 cm2 ≈ 41.3 cm2

33. 900√3 m2 ≈ 1558.8 m2

Pg 5612. 84.3 in2

6. 150√3 = 259.8 ft210. 151 m2

14. 311.3 km2

18. (a) 50 mm2; (b) 116 mm2

22. P = 45.3 in; A = 128 in2

26. P = 6.2 mi; A = 3 mi220. 1,459,000 ft223. P = 17.6 ft; A = 21.4 ft233. 5.0 ft236. 320 ft

10-4: Answers to Pg 555 # 2-8 evens, 9, 10-32 evens, 25, 40-44.

2. 4:3, 16:94. 3:5, 9:256. 54 m2

8. 439 m2

9. $38410. $47.2012. 5:2, 5:214. 3:4, 3:416. 1:10, 1:1018. 2:5, 4:2520. 7:4, 49:16

22. C24. 0.3 cm2

26. x = 2 cm, y = 3 cm28. x = 4 cm, y = 6 cm30. x = 4√2 cm, y = 6√2 cm32. 2.25 in by 12 in, 3 in by 16 in.25. 252 m2

40. a) 6√3 cm2. b) 54√3 cm2, 13.5√3 cm2, 96√3 cm2.

41. always42. sometimes43. never44. sometimes

10-6: Answers to Pg 569 # 8, 15-60 (multiples of 5, omit #40), 51, 59-66, 70-72

8. 126°15. 128°20. 308°25. 142°30. 14π in.35. 8π ft.45. 55°50. (a) 0.5°. (b) 2.5°. (c) 10°55. 50 in.60. (a) 25,000 mi. (b). The

estimate seems quite accurate.

51. 100°59. 105 ft

60. a) 25,000 mi. b) Eratosthenes’s estimate seems quite accurate.

61. (2.5, 5)62. 5π units63. 5.125π ft64. 2.6π in65. 3π m66. 44.0 cm70. (a) arcs BD and FE, or arcs

AB and GF, or etc. (b) x=35. 71. 2π in.72. 325.7 yd, 333.5 yd, 341.4

yd, 349.2 yd, 357.1 yd, 365.0 yd, 372.8 yd, 380.6 yd.

10-7: Answers to Pg 577 # 2-26 evens, 28-32 all, 35-38 all, 40

2. 30.25π cm2

4. π / 9 in2

6. about 22 ft28. 64π cm2

10. 12π in2

12. 56π cm2

14. 1.5π ft216. 28.125π cm2

18. 18.3 ft220. 20.4 m2

22. (243π +162) ft224. (120π + 36√3) m2

26. (64 – 16π) ft228. A

29. Lower outside has larger base area (8.75π in2) than Top and Lower inside (8π in2)

30. 9 circles31. 15.7 in2

32. 12 in.35. (49π – 73.5√3) m2

36. (200 – 50π) m2

37. 4π m2

38. Blue region; let AB = 2x. Area of blue = 4x2 – πx2. Area of yellow = πx2 – 2x2.

40. (c) 239 ft2.

10-8 Answers to Pg 584 # 4, 6, 7, 10, 16, 18, 20-28 all, 32-34 all, 38-44 even.

4. 2/5 or 40%6. 3/10 or 30%7. 2/5 or 40%

10. 4/7 or about 57%16. 25%18. 2/3 or about 67%20. (4 – π)/4 or about 21%21. 4%22. 623. π/424. π/4

25. π/426. 10π/200 or about 16%27. a) 14 prizes. b) $110.28. 3/5 or 60%

32. 3/533. 3/1034. 9/20 or 45%38. 3/1040. about 46%42. about 58%44. a) yes. b) no. c) 2/3

Review: Similarity and Right Triangles Name: ___________________________ G.11A, G.11B, G.8C, G.5D, G.11C Date: ________________ Period: _____

Similarity: TEKS: G.11A – The student will use and extend similarity properties and transformations to explore and justify conjectures about geometric figures. TEKS: G.11B – The student will use ratios to solve problems involving similar figures. 1. A triangle has side lengths 1, 1.5, and 2 units. Which of the following could be the lengths of the sides of a triangle that was formed by dilating the given triangle? A. 1, 3, and 4 units B. 2, 4, and 6 units C. 4, 4.5 and 5 units D. 4, 6, and 8 units

2. Ramon places a mirror on the ground 45 ft from the base of a geyser. He walks backward until he can see the top of the geyser in the middle of the mirror. At that point, Ramon’s eyes are 6 ft above the ground and he is 7.5 ft from the mirror. Use similar triangles to find the height of the geyser.

3. 4.

x ft

7.5 ft

6 ft

45 ft

Pythagorean Theorem: TEKS: G.8C – The student will derive, extend, and use the Pythagorean theorem. 5. Find the area and perimeter of the following trapezoid.

6. Look at the drawing shown below. If ΔKMP is a right triangle formed by the placement of 3 squares, what is the area of the shaded square?

7. A parallelogram has sides measuring 8.5 cm and 12 cm and a diagonal measuring 15 cm. Is the parallelogram a rectangle? If not, is the 15 cm diagonal the longer or shorter diagonal?

16

4 x

18

8. Oscar's dog house is shaped like a tent. The slanted sides are both 5 feet long and the bottom of the house is 6 feet across. What is the height of his dog house, in feet, at its tallest point?

9. What type of triangle is formed by these side lengths:

8, 15, 17 50, 120, 130 1.41, 1.73, 2.23 9, 12, 18

Special Right Triangles: TEKS: G.5D – The student will identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples. 10. Find the length of the diagonal of a square with perimeter 56. 12.

11. Charles is looking out a window from a point 50 feet above the ground. When Charles looks down at an angle of depression of 30°, he sees his dog Max. To the nearest foot, how far is Max from the base of the building?

30°

x

50 feet

Max

Charles

12

y

x

Trigonometry: TEKS: G.11C – The student will develop, apply, and justify triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples using a variety of methods. 13. Mr. Ryan flies in his airplane at an altitude of 2400 ft. He sees a cornfield at an angle of depression of 30°. What is his approximate horizontal distance from the cornfield at this point?

Cornfield

30°Airplane

2400 ft

14. A man who is 6 feet tall is flying a kite. The kite string is 75 feet long. If the angle that the kite string makes with the line horizontal to the ground is 35°, how far above the ground is the kite?

15. A 12-foot ladder is leaning against a wall. If it is 4 feet from the base of the wall, what is the angle the ladder makes with the ground?

16. A tree has a shadow that is 31 feet long. If the angle created by the end of the shadow and the sun is 62°, how tall is the tree?

Name: ___________________________ Date: ________________ Period: _____

17. What is the approximate length of FJ ?

8 inches

8 inches

5 inches

J

FG

H

18. Melissa is looking at a tall tree in her backyard at a 68° angle. She is standing 20 feet from the base of the tree. How tall is the tree?

19. (a) Determine whether the two triangles are similar. (b) If they are similar, state the theorem or postulate used to justify similarity. (c) Write the similarity statement. (d) Solve for x. ∆LMN ~ ∆__________ by __________

20. A kite string is 220 feet long from the kite to the ground. The string makes a 45° angle with the ground. About how high off the ground is the kite?

21. Solve for x and y.

22. Find the amount of fencing needed for a rectangular yard with a diagonal of 39 m and one side of 36 m.

23. The diagram shows a portion of a bridge support. What is the distance from point B to point C?

100 ft40 ft120 ft

DE

C

B

A

24. A sailor in a boat is looking at the top of a 150-foot tall lighthouse that is 280 feet away. What is the angle of depression from the top of the lighthouse down to the sailor?

x

y

12

4

25. Mr. Schultz has a garden shaped like an equilateral triangle that measures 11 feet on each side. He has placed a watering hose that extends from the faucet located at a vertex to the opposite side, as shown below. Which is closest to the length of the hose in the garden?

26) ΔKLP has vertices K (−4, 2), L (2, 6), and P (4, −6). It is dilated to form ΔK′L′P′ with the origin as the center of dilation. If the coordinates of K′ are (−6, 3), what scale factor was used to form ΔK′L′P′?

F 23

G 14

H 32

J 4

27. The numbers represent the lengths of the sides of a triangle. Classify each triangle as acute, obtuse or right: a.) 6, 9, 10 b.) 18, 24, 30 c.) 20, 100, 110

28. Find x, y and z.

60°

29. Solve for x and y.

30. The diagonal of a square measures 32 meters. What is the area of the square?

31. Mr. Carpenter built a wooden gate, as shown below. Which is closest to the length in feet of the diagonal board that Mr. Carpenter used to brace the wooden gate?

32. If ||AB ED and AD BE⊥ , what is the

measure of EB ?

25 m

10 m

6 m

E D

C

BA

Review for Pre-AP Test 3.4 Name: ___________________________ Cumulative 3rd Nine-Week Test Date: ________________ Period: _____ Review all 3 previous tests in the 3rd 9-wks! (Proofs will not be on the test.) Give answers in simplest exact form. 1. In quadrilateral ABCD, AB = 5, BC = 17, CD = 5, DA = 9. What inequality best describes the range of lengths for BD?

If BD is an integer, what is BD?

2. Find the area and perimeter of the triangle RST.

3. Find the area and perimeter of the rhombus. Leave your answer in simplest radical form.

60°

5

Not drawn to scale

4. What is the area and perimeter of the non-shaded part of the rectangle below?

5. The lengths of the bases of an isosceles trapezoid are shown below. If the perimeter of this trapezoid is 32 units, what is its area?

What is the angle measure of the top left vertex? What is the angle measure of the bottom right vertex?

6. The top view of the floor of an office building is shown. It consists of part of a circle and two regular polygons. If the radius of the circle is 12 ft. and carpet costs $12 a square yard, $50 for removing the old carpet, and $75 for installing the new carpet, how much would it cost to recarpet the floor?

7. Find the area and perimeter of the figure below (a regular hexagon with semicircles attached).

8. AF=FG, and FC=ED=FE=CD. Find the area and perimeter of the figure.

100 ft 135º

300 ft

A B

C

DE

FG

9

semicircle

15

8

9. Quadrilateral WXYZ is a parallelogram with WY and XZ intersecting at point E. WX = 2x – 1, XY = x + 7, YZ = 6y – 5, WZ = 5y + 1. Find WX and WZ.

10. Find the area of the quadrilateral ABCD with coordinates A(-1,5), B(6,4), C(2,-2), D(-5,2).

Find new coordinates for D (_____, _____) so that ABCD is a parallelogram.

11. Find the area of the shaded sector?

12. A satellite moves in a nearly circular orbit around Earth, completing an orbit every 24 hours. The radius of the orbit is about 42,000 km. At 1 p.m. the satellite is at point A. At 5 p.m. the satellite is at point B. Approximately how many kilometers does the satellite travel between 1 and 5 p.m.?

13. Doris had a circular garden with a radius of 30 feet. She used all of the fencing from the circular garden to enclose a square garden. What was the approximate length of each side of Doris’s square garden?

14. The area of this regular polygon is 72 square inches. Find the approximate length of one side of this polygon (round to the nearest thousandth).

15. A developer wanted to blacktop the shaded portion of this corner building site. How much will it cost if blacktopping costs $5 per square meter?

16. A city planner measured the distances shown from the old oak, the big rock, and the flag to the east-west line. Other distances along the line are shown. What is the area of the city park? (Hint: Enclose the park with a rectangle.)

48 m 16 m

17. The shorter diagonal of a rhombus has the same length as a side. Find the area if the longer diagonal is 12 cm. long.

18. Find the total area of the parallelogram. (Hint: Find the area of one triangle first.)

164 m

Flag

Big Rock

Old Oak City Park

126 m 83 m

106 m 48 m 62 m W E

14 m

8 m

17

8 8

17