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363Geometry

Chapter 11 Resource Book

LESSON

11.6 Practice BFor use with pages 792–799

Find the measure of a central angle of a regular polygon with the given number of sides. Round answers to the nearest tenth of a degree, if necessary.

1. 20 sides 2. 36 sides 3. 120 sides 4. 23 sides

Find the given angle measure for the regular dodecagon shown.

5. m∠ TWU 6. m∠ TWX JK

L

M

NP

VU

T

S

R

W

X 7. m∠ XUW 8. m∠ TWK

9. m∠ UWK 10. m∠ XWK

11. Multiple Choice Which expression gives the apothem for a regular nonagon with side length 10.5?

A. a 5 5.25

} tan 408

B. a 5 10.5

} tan 208

C. a 5 5.25

} tan 208

D. a 5 5.25 p tan 208

12. A regular hexagon has diameter 22 inches. What is the length of its apothem? Round your answer to the nearest tenth.

13. A regular octagon has diameter 8.5 feet. What is the length of its apothem? Round your answer to the nearest tenth.

Find the perimeter and area of the regular polygon. Round answers to the nearest tenth, if necessary.

14.

8

15.

20

16.

5

17.

4.5

18.

5

19.

2.5

20. What is the area of a regular 18-gon with a side length of 8 meters? Round your answer to the nearest tenth, if necessary.

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364GeometryChapter 11 Resource Book

LESSON

0.0

21. What is the area of a regular 24-gon with a side length of 10 inches? Round your answer to the nearest tenth, if necessary.

22. What is the area of a regular 30-gon with a radius of 20 feet? Round your answer to the nearest tenth, if necessary.

23. Find the area of a regular pentagon inscribed in a circle whose equation is given by (x 2 4)2 1 (y 2 6)2 5 16.

24. Find the area of a regular octagon inscribed in a circle whose equation is given by (x 2 2)2 1 (y 1 3)2 5 25.

Find the area of the shaded region. Round answers to the nearest tenth, if necessary.

25. 16

26.

10

27.

40°

12

28.

72° 16

In Exercises 29 and 30, use the following information.

Tiles You are tiling the fl oor of a hallway with tiles that are

6 in.

regular hexagons as shown.

29. What is the area of each tile?

30. The hallway has a width of 5 feet and a length of 12 feet. At least how many tiles will you need?

31. A cup saucer is shaped like a regular decagon with a

5.5 in.

diameter of 5.5 inches as shown.

a. What is the length of the apothem of the saucer? Round your answer to the nearest tenth.

b. What is the perimeter and area of the saucer? Round your answers to the nearest tenth.

LESSON

11.6 Practice B continuedFor use with pages 792–799

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A54GeometryChapter 11 Resource Book

15. about 88.59 m 16. about 378

17. about 9.11 m 18. about 37.31 m

19. about 107.68 m 20. about 31.42 m2

21. about 31.32 m2 22. about 70.69 in.2

23. about 110.01 in.2 24. about 219.75 cm2

25. about 12.57 cm2 26. c. 16-inch pizza

27. They all waste the same amount of paper.

Review for Mastery

1. A < 95 cm2 2. r < 7.1 yd 3. d 5 64 m

4. 423.12 m2 and 961.63 m2 5. 634.89 m2

Challenge Practice

1. 50 π

} 3 2 25 Ï

}

3 < 9.1 cm2

2. 81 π

} 2 2 81 Ï

}

2 < 12.7 in.2 3. 20.2 ft2

4. 36 Ï}

3 2 18π < 5.8 cm2

5. 1369π < 4300.8 in.2

6. a.

x 308 608 908 1208 1508 1808

y 3 π

} 4

3 π }

2

9 π }

4 3π

15 π }

4

9 π }

2

b.

0 60 120 180 x0

y

Measure of arc(degrees)

Are

a o

f se

cto

r(s

qu

are

inch

es)

p

2p

3p

4p

The data appear to follow a linear pattern.

c. y 5 π

} 40

x

Lesson 11.6

Practice Level A

1. 308 2. 22.58 3. 98 4. 17.18 5. 608

6. 908 7. 308 8. 1208 9. 6.1 in. 10. 8.3 ft

11. 64 square units 12. about 41.6 square units

13. about 58.1 square units 14. about 187.1 square units 15. about 1039.2 square units

16. about 152.8 square units 17. 277.0 m2

18. 906.9 cm2 19. 688.8 ft2 20. 24 units; 41.6 square units 21. 45.3 units; 128 square units

22. 53.0 units; 212.1 square units 23. 41.6 units; 83.1 square units 24. 33.9 units; 72 square units

25. 72.7 units; 363.3 square units 26. false

27. true 28. false 29. a. 458 b. 15 in.; about 16.2 in.; 744 in.2 30. about 15.5 in.2

Practice Level B

1. 188 2. 108 3. 38 4. 15.78 5. 308 6. 158

7. 758 8. 1208 9. 908 10. 1058 11. C

12. 9.5 in. 13. 3.9 ft 14. 48 units; 166.2 square units 15. 100 units; 688.2 square units 16. 30.4 units; 68.4 square units 17. 29.8 units; 68.4 square units 18. 60 units; 279.9 square units

19. 16.4 units; 20.5 square units 20. 1633.3 m2

21. 4557.5 in.2 22. 1247.5 ft2

23. 38.0 square units 24. 70.7 square units

25. 139.1 square units 26. 184.3 square units

27. 4.0 square units 28. 28.3 square units

29. 93.5 in.2 30. at least 93 tiles 31. a. 2.6 in. b. 17.0 in.; 22.2 square units

Practice Level C

1. 248 2. 14.48 3. 11.38 4. 5.18 5. 10.6 in.

6. 16.6 m 7. about 70.1 square units 8. about 400.5 square units 9. about 1014.8 square units

10. 292.3 cm2 11. 187.7 in.2 12. 19.8 cm2

13. 6.2 cm 14. 60 units; 247.7 square units

15. 59.6 units; 268.4 square units 16. 43.3 units; 144.0 square units 17. 72 units; 374.1 square units 18. 73.5 units; 407.3 square units

19. 74.2 units; 423.2 square units 20. always 21. always 22. never 23. about 6.9 in.2

24. about 41.6 in.2 25. about 22.2% 26. $9.36

27. a. 3 colors b. about 166.3 in.2 c. about 28 tiles

Review for Mastery

1. 408 2. 208 3. 908 4. P < 51.25 units; A ø 179.37 square units 5. P < 17.63 units; A < 21.40 square units 6. P 5 48 units; A < 173.82 square units

Challenge Practice

1. about 110.1 cm2 2. A 5 n cos 1 180 }

n 2 8sin 1 180

} n 2 8

Lesson 11.5, continuedA

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