Name ———————————————————————
Date ————————————
Practice B
LESSON
11.3
For use with pages 765–771
Complete the table of ratios for similar polygons.
Ratio of corresponding side lengths
1.
Ratio of perimeters
Ratio of areas
5:8
2.
4:7
3.
169 : 36
4.
66 : 18 5 ?
Corresponding lengths in similar figures are given. Find the ratios (shaded
to unshaded) of the perimeters and areas. Find the unknown area.
5.
A 5 2 ft2
2 ft
5 ft
6.
A 5 400 in.2
20 in.
7.
8. A 5 1024 mm2
A 5 162 cm2
22 cm
18 cm
24 mm
9 mm
The ratio of the areas of two similar figures is given. Write the ratio of the
lengths of corresponding sides.
9. Ratio of areas 5 16 : 81
10. Ratio of areas 5 25 : 196
11. Ratio of areas 5 144 : 49
LESSON 11.3
Use the given area to find XY.
330
12. ABCD , WXYZ
B
13. EFGHJK , UVWXYZ
15 in.
V
C
X
A
A 5 135 in.2
Geometry
Chapter 11 Resource Book
D
W
Y
Z
A 5 15 in.2
F
E
W
G
H
8 cm
K J
A 5 168 cm2
U
X
Z
Y
A 5 378 cm2
Copyright © Holt McDougal. All rights reserved.
14 in.
Name ———————————————————————
LESSON
11.3
Practice B
For use with pages 765–771
Date ————————————
continued
14. Regular octagon ABCDEFGH has a side length of 10 millimeters and an
area of 160 square millimeters. Regular octagon JKLMNOPQ has a perimeter
of 200 millimeters. Find its area.
15. Kites RSTU and VWXY are similar. The area of RSTU is 162 square feet. The
diagonals of VWXY are 32 feet long and 18 feet long. Find the area of VWXY.
Then use the ratio of the areas to find the lengths of the diagonals of RSTU.
16. n ABC and n DEF are similar. The height of n ABC is 42 inches. The base of
n DEF is 7 inches and the area is 42 square inches. Find the ratio of the area
of n ABC to the area of n DEF.
17. Rectangles ABCD and EFGH are similar. The width of ABCD is 18 centimeters and
the perimeter is 120 centimeters. The length of EFGH is 91 centimeters. Find the
ratio of the side lengths of ABCD to the side lengths of EFGH.
18. Posters Your school had a car wash to raise money.
A poster that was used to attract customers is shown.
You decide that you will have the car wash again
next year. You will have a similar poster but you
will increase the length to 6 feet to try to attract
more customers. Find the area of the new poster.
2 ft
4 ft
the large rug is priced fairly. The price of the small rug is $84. The price of the large
rug is $210.
a. What are the areas of the two rugs? What is the ratio of the area of the small rug
to the area of the large rug?
b. Compare the rug costs. Do you think the large rug is a good buy? Explain.
5 ft
10 ft
8 ft
12 ft
LESSON 11.3
Copyright © Holt McDougal. All rights reserved.
19. Rug Costs You are comparing the two rugs shown below. You want to be sure that
Geometry
Chapter 11 Resource Book
331
Lesson 11.3, continued
6. 3 : 5; 9 : 25; 81 in.2 7. 9 : 5; 81 : 25; 50 m2
4. a. 2340 ft2 b. 280.8 ft c. 3369.6 ft2; 1029.6 ft2
8. 3 : 5 9. 4 : 7 10. 6 : 2 11. 5 in. 12. 18 cm
5. Answers will vary. 6. 1496 ft2 7. The area
16. sometimes 17. 25 : 64 18. 4 : 3 19. 4 : 5
20. 100 in.2 21. 60 ft 22. 32 ft
Practice Level B
1. 5 : 8; 25 : 64 2. 4 : 7; 16 : 49 3. 13 : 6; 13 : 6
4. 11 : 3; 11 : 3; 121 : 9 5. 2 : 5; 4 : 25; 12.5 ft2
6. 7 : 10; 49 : 100; 196 in.2 7. 11 : 9; 121 : 81;
242 cm2 8. 8 : 3; 64 : 9; 144 mm2 9. 4 : 9
10. 5 : 14 11. 12 : 7 12. 5 in. 13. 12 cm
14. 1000 mm2 15. 288 ft2; 24 ft and 13.5 ft
16. 49 : 4 17. 6 : 13 18. 18 ft2 19. a. 40 ft2
and 120 ft2; 1 : 3 b. Yes; The area of the larger rug
Challenge Practice
3
1. x 5 2 2. x 5 5 3. x 5 7 4. x 5 }
2
5. x 5 4, y 5 4 6. x 5 8, y 5 3
3
7. x 5 }, y 5 10 8. x 5 5, y 5 6
2
is 3 times the area of the smaller rug, but it is only
2.5 times the cost.
Lesson 11.4
Practice Level C
Practice Level A
1. 4 : 7; 16 : 49; 144 in.2 2. 2 : 5; 4 : 25; 450 cm2
1. about 43.98 cm 2. about 62.83 ft
3. 10 : 7; 100 : 49; 85.75 mm2
18
29
3. about 7.64 in. 4. } m 5. } ft 6. 26π in.
π
π
}
4. 8 : 3; 64 : 9; 384 ft2 5. 13 : 12 6. 2Ï 7 : 7
}
}
7. 5Ï 5 : 6Ï 3 8. 8 in. 9. 15 cm 10. 81 : 64
}
7. 30π cm 8. about 11 in. 9. about 12.57 ft
}
10. about 9.42 cm 11. 3208 12. 1608
}
13. about 22.34 in. 14. about 11.17 in. 15. 2008
11. 4 : 9 12. 360 in.2 13. 8Ï 2 cm by 12Ï 2 cm
14. 216 ft 2; 32 ft and 24 ft; 20 ft 15. 216Ï 3 mm2
16. 6 17. 16 18. 75 square units 19. 6
20. 10 21. 192 square units 22. No; You are
charged a higher home rate ($.05/ft 2) than your
company rate ($.03/ft 2).
Review for Mastery
4
1. }; 54 ft2 2. 8 ft 3. about 10.7 cm
9
}
16. about 13.96 in. 17. about 23.56 cm
18. 90 in. 19. 36 in. 20. 58.27 21. 24.57
22. 3.14; 1108; 8.5; 5; 808; 53.15
23. a. about 14.14 in. b. 177 ft 24. 16 in.
Practice Level B
21
1. 50.27 ft 2. 40.84 in. 3. 10.50 cm 4. } m
π
39
5. } cm 6. 15π in. 7. 54π ft 8. 6.28 cm
π
4. 3Ï 10 : 25
Problem Solving Workshop:
Mixed Problem Solving
}
1. a. 1 : 3 b. 1 : Ï 3 c. about 14 in. d. about 6 in.
2. a. 1500 in.2, 9375 in.2; 25 : 4
b. The dimensions of the large rug are increased
by a scale factor of 2.5 from the small rug. The
price of the large rug is 2.375 times as much as
the price of the small rug, so the large rug is a
good buy. By comparing the areas, the large rug is
a good buy because the large rug has an area that
is 6.25 times greater than the area of the small rug
and a price that is only 2.375 times greater.
3. Answers will vary.
A52
doubles; the area triples; the area increases by a
factor of n. When you substitute nb1 for b1 and
nb2 for b2 in the equation for the area of a
trapezoid, you can factor out an n and get n times
the area of the original trapezoid, which means
that the area of a trapezoid when each base is
multiplied by n is n times greater than the original
area of the trapezoid.
Geometry
Chapter 11 Resource Book
9. 47.12 in. 10. 7.33 ft 11. 1608 12. 2008
13. 19.55 m 14. 24.43 m 15. 2808
16. 34.21 m 17. 114.028 18. 58.03 ft
19. 20.53 cm 20. 45.71 mm 21. 138.56 in.
22. 2.09; 43.02°; 9.79; 4.81; 88.24°; 50.42
23. a. about 35.61 in. b. about 71 teeth
24. about 56.55 ft
Practice Level C
1. about 35.81 cm 2. about 67.86 ft
37
58
3. about 14.96 in. 4. } 5. } 6. 26.3π
π
π
Copyright © Holt McDougal. All rights reserved.
ANSWERS
13. sometimes 14. always 15. always