CHAPTER 8
Chapter Opener
28. Yes. Opposite sides of a parallelogram are congruent,
so all four sides are congruent and the parallelogram is
equilateral.
Chapter Readiness Quiz (p. 410)
1. A; a rhombus has four congruent sides.
29. Yes. Sample answer:
30. Yes. Sample answer:
31. Yes. Sample answer:
32. Yes. Sample answer:
33. 3 in. 5 15 in.
34. 7 cm 8 56 cm
2. H
Lesson 8.1
8.1 Checkpoint (p. 412)
1. Convex; the polygon is not regular because it is equilateral
but not equiangular.
2. Concave; the polygon is not regular because it is equilateral
but not equiangular.
3. Convex; the polygon is regular because it is both equilateral
and equiangular.
35. 4 ft 12 48 ft
36. 2x 120
8.1 Guided Practice (p. 413)
37. x 9 15
x 60
1. Sample answer:
x6
38. 5x 5 60
5x 65
x 13
2. All the sides of an equilateral polygon are congruent, while
8.1 Standardized Test Practice (p. 415)
all the angles of an equiangular polygon are congruent.
3. A regular polygon is both equilateral and equiangular.
4. convex
7. C
5. concave
8. A
6. convex
9. B
39. A
40. H
8.1 Mixed Review (p. 415)
41. Yes; the figure has five sides so it is a pentagon.
8.1 Practice and Applications (pp. 413–415)
42. Yes; the figure has four sides so it is a quadrilateral.
43. Yes; the figure has eight sides so it is an octagon.
10. convex
13. equiangular
11. concave
12. concave
14. equilateral
15. neither
8.1 Algebra Skills (p. 415)
16. Not regular; the polygon is equilateral but not equiangular.
44. 52 5 5 25
45. (4)2 (4) (4) 16
17. Regular; the polygon is both equilateral and equiangular.
46. 6 6 6 6 216
47. 25 2 2 2 2 2 32
18. Not regular; the polygon is equilateral but not equiangular.
48. 兹3
苶6
苶 兹6
苶2苶 6
49. 兹1
苶 兹1苶2苶 1
19. Regular; the polygon is both equilateral and equiangular.
50. 兹1
苶6
苶9
苶 兹1
苶3苶苶2 13
51. 兹5
苶 ⬇ 2.2
20. Regular; the polygon is both equilateral and equiangular.
21. Not regular; the polygon is equiangular but not equilateral.
22. concave
23. concave
24. convex
25. Polygon C is convex; polygons A and B are concave.
26. No. Sample answer: None of the polygons appear to be
3
Lesson 8.2
8.2 Activity (p. 416)
Step 3.
Polygon
both equilateral and equiangular.
27. Yes. The sum of the measures of the angles of a
triangle is 180. So, the missing angle measure is
180 60 60 60. All three angles are congruent,
so the triangle is equiangular.
Copyright © McDougal Littell Inc.
All rights reserved.
Number of Number of Sum of measures
sides
triangles of interior angles
Triangle
3
1
1 180 180
Quadrilateral
4
2
2 180 360
Pentagon
5
3
3 180 540
Hexagon
6
4
4 180 720
Geometry, Concepts and Skills
Chapter 8 Worked-Out Solution Key
119
Chapter 8 continued
1. 5 180 900; 6 180 1080
8.2 Practice and Applications (pp. 421–423)
2. (n 2) 180
8. (n 2) 180 (6 2) 180 4 180 720
9. (n 2) 180 (8 2) 180 6 180 1080
8.2 Checkpoint (pp. 418–420)
1. (n 2) 180 (5 2) 180 3 180 540;
111 118 130 109 ma G 540
468 ma G 540
ma G 72
2. (n 2) 180 (4 2) 180 2 180 360;
58 133 103 ma G 360
10. (n 2) 180 (4 2) 180 2 180 360
11. (n 2) 180 (10 2) 180 8 180 1440
12. (n 2) 180 (15 2) 180 13 180 2340
13. (n 2) 180 (20 2) 180 18 180 3240
14. (n 2) 180 (30 2) 180 28 180 5040
15. (n 2) 180 (52 2) 180 50 180 9000
16. (n 2) 180 (100 2) 180 98 180 17,640
294 ma G 360
17. (n 2) 180 (4 2) 180 2 180 360;
ma G 66
3. (n 2) 180 (7 2) 180 5 180 900;
140 140 90 130 150 120 ma G 900
770 ma G 900
ma G 130
4. (n 2) 180 (12 2) 180 10 180 1800;
1800
150
12
5. 73 90 60 x 46 360
x 269 360
x 91
6. 89 3x 116 92 360
3x 297 360
ma A 92 68 101 360
ma A 261 360
ma A 99
18. (n 2) 180 (6 2) 180 4 180 720;
ma A 110 149 91 135 100 720
ma A 585 720
ma A 135
19. (n 2) 180 (5 2) 180 3 180 540;
ma A 90 130 80 113 540
ma A 413 540
ma A 127
20. (n 2) 180 (6 2) 180 4 180 720;
3x 63
ma A 102 146 120 124 158 720
x 21
ma A 650 720
7. x x 110 360
ma A 70
2x 110 360
21. (n 2) 180 (6 2) 180 4 180 720;
2x 250
720
120
6
22. (n 2) 180 (7 2) 180 5 180 900;
900
⬇ 128.6
7
23. (n 2) 180 (3 2) 180 1 180 180;
180
60
3
24. 75 44 65 x 76 54 360
x 125
8. 70 3x 75 65 2x 360
5x 210 360
5x 150
x 30
8.2 Guided Practice (p. 420)
1. Any one of : a A, a B, a BCD, a D, a DEA;
any one of: a FEA, a DCH, a BCG
2. (n 2) 180
3. (n 2) 180 (9 2) 180 7 180 1260
4. ma 1 65 40 180
5. ma 1 66 130 100 360
x 314 360
x 46
25. 2x 71 85 44 3x 360
5x 200 360
5x 160
x 32
6. ma 1 115 86 89 360
26. No; it is not equilateral or equiangular.
7. ma 1 117 57 59 85 360
27. (n 2) 180 (5 2) 180 3 180 540
120
Geometry, Concepts and Skills
Chapter 8 Worked-Out Solution Key
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 8 continued
28. 90 90 x 90 x 540
43.
270 2x 540
2x 270
x 135
ma C ma E 135
29. (n 2) 180 (5 2) 180 3 180 540;
540
108
5
30. Answers will vary.
2
2
2
BE BD (52) 34;
3
3
3
BD BE ED
2
52 34 ED
3
1
17 ED
3
8.2 Algebra Skills (p. 423)
31. The sum of the measures of the exterior angles of a
convex polygon is always 360.
32. The sum of the measures of the interior angles of a
44. ⏐5⏐ 5
45. ⏐11⏐ 11
46. ⏐48⏐ 48
47. ⏐0⏐ 0
48. ⏐13.2⏐ 13.2
49. ⏐2⏐ 2
50. ⏐0.001⏐ 0.001
51. ⏐1.11⏐ 1.11
convex octagon is never 1440;
(n 2) 180 (8 2) 180 6 180 1080
33. The measures of the exterior angles of a convex polygon
are sometimes equal.
720
120
120; 60;
6
2
ma 1 ma 2 60
360
n
360 60n
3. Not regular; the polygon is neither equilateral nor
equiangular.
4. (n 2) 180 (5 2) 180 3 180 540;
360
n
360 20n
36. 20
6n
360
37. 72
n
360 72n
1. Not regular; the polygon is equilateral but not equiangular.
2. Regular; the polygon is both equilateral and equiangular.
34. (n 2) 180 (6 2) 180 4 180 720;
35. 60
Quiz 1 (p. 423)
18 n
360
38. 10
n
360 10n
5n
36 n
ma 1 92 120 76 112 540
ma 1 400 540
ma 1 140
5. (n 2) 180 (6 2) 180 4 180 720;
ma 1 140 100 120 140 100 720
ma 1 600 720
ma 1 120
6. ma 1 104 79 68 360
ma 1 251 360
8.2 Standardized Test Practice (p. 423)
ma 1 109
39. B; (n 2) 180 (6 2) 180 4 180 720
x 134 120 102 2x 130 720
7. ma 1 93 74 92 360
3x 486 720
ma 1 259 360
3x 234
ma 1 101
x 78
8. ma 1 50 61 95 44 360
ma 1 250 360
40. H; ma P 2x 2(78) 156
ma 1 110
8.2 Mixed Review (p. 423)
2
2
3
3
BD BE ED
41. BE BD (6) 4;
6 4 ED
2 ED
2
2
42. BE BD (33) 22;
3
3
BD BE ED
33 22 ED
11 ED
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Lesson 8.3
8.3 Checkpoint (pp. 425–426)
1. A bh
2. A bh
11 11
62
121 m
12 ft2
2
3. A bh
5.9 4.5
26.55 yd2
4.
A bh
52 4b
13 m b
Geometry, Concepts and Skills
Chapter 8 Worked-Out Solution Key
121
Chapter 8 continued
5. A bh bh
16.
(7)(3) (7 4)(6 3)
8 ft
(7)(3) (3)(3)
21 9
13 ft
30 in.2
A bh 13 8 104 ft2
6. A bh bh bh
(4)(3) (12)(6 3) (3)(5 3)
(4)(3) (12)(3) (3)(2)
17. A bh 14 14 196 m2
18. A bh 7 7 49 m2
19. A bh 9 9 81 m2
12 36 6
20.
54 m2
A bh
A bh
21.
56 8h
54 b 18
7 in. h
8.3 Guided Practice (p. 427)
22.
1. rectangle
3 cm b
A bh
33 6.6h
2. C; A bh (2x)(2x) 4x
2
5 ft h
3. A; A bh (x)(x) x2
4. B; A bh (2x)(x) 2x2
23. Yes. Since the perimeter is 28 feet, each side measures
5. True; the area of the polygon is
Area A Area B Area C.
6. False; the height of Rectangle A is 7 3 2 2 units.
7. True; the height of Rectangle C is 3 2 5 units.
8.3 Practice and Applications (pp. 427–429)
8. A bh 6 6 36 ft2
28 4 7 feet, Area 72 49 square feet.
24. b 11 4 2 5 ft,
h 3 ft
25. b 11 2 4 2 3 ft,
h 6 ft
26. b 4 ft
h (6 2) 3 4 3 7 ft
9. A bh 12 12 144 m2
27. A bh bh
10. A bh 20 20 400 in.2
(12 7)(5) (7)(10)
11. A bh 5 2 10 cm2
(5)(5) (7)(10)
12. A bh 6 7 42 yd2
25 70
13. A bh 12.1 5 60.5 m2
95 m2
14.
28. A bh bh
(4)(8 3) (4 5)(3)
(4)(5) (9)(3)
20 27
2.2 cm
A bh 2.2 2.2 4.84 cm
2
47 in.2
29. A bh bh
15.
(16 7)(9) (7)(5)
(9)(9) (7)(5)
11 m
81 35
116 yd2
30. A bh bh bh
(4)(12) (18 4)(11 5) (18 4 10)(5)
4m
A bh 4 11 44 m2
(4)(12) (14)(6) (4)(5)
48 84 20
152 cm2
122
Geometry, Concepts and Skills
Chapter 8 Worked-Out Solution Key
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 8 continued
31. A bh bh
8.3 Algebra Skills (p. 429)
(450)(400) (450 175)(500 400)
41. 8 18
42. 2459 2495
(450)(400) (275)(100)
43. 10 0
44. 1.12 1.01
180,000 27,500
45. 2.44 2.04
46. 0.75 0.7
207,500 ft
2
1 acre
32. 207,500 ft2 2 ⬇ 4.76 acres
43,560 ft
$34
$57
33. C 4.76 acres 4.76 acres
acre
acre
$161.84 $271.32
$433.16
8.4 Activity (p. 430)
1. yes
2. The area of the triangle is half the area of the rectangle.
3. Answers will vary.
8.3 Standardized Test Practice (p. 429)
34. a. A bh bh
7x 6x
13x
1
2
1
5. A (14)(6) 42 ft2
2
4. A bh
8.4 Checkpoint (p. 433)
1
1
2
2
1
1
2. A bh (12)(7) 42 yd2
2
2
1
1
3. A bh (15)(16) 120 cm2
2
2
1
4.
A bh
2
1
84 b(14)
2
168 14b
1. A bh (9)(8) 36 in.2
b. 13x 65
x 5 units
c.
Lesson 8.4
7
5
6
5
12 in. b
8.3 Mixed Review (p. 429)
AE (Diagonals of a g bisect each other.)
35. C; CE
**** ⬵ ****
36. A; CD
AB (Opposite sides of a g are ⬵.)
**** ⬵ ****
37. D; a ABD ⬵ a CDB (If two parallel lines are cut by a
transversal, then alternate interior angles are congruent.)
8.4 Guided Practice (p. 434)
1. base 9ft, height 5 ft
2.
38. B; a CBA ⬵ a ADC (Opposite angles of a g are ⬵.)
3.
7
7
39. Yes; a U ⬵ a R; also, the ratios of the sides that include
a U and a R are equal.
6
63
2
shorter sides: 15
15 3
5
10
10 5
2
longer sides: 25
25 5
5
So, T SUT ⬃ T PRQ by the SAS Similarity Theorem.
9
93
3
40. No; shortest sides: 6
63
2
18
18 2
9
longest sides: 10
10 2
5
10
10 2
5
remaining sides: 8
82
4
Copyright © McDougal Littell Inc.
All rights reserved.
15
15
4.
7
15
8.4 Practice and Applications (pp. 434 –437)
1
1
2
2
1
1
6. A bh (7)(6) 21 ft2
2
2
1
1
15
7. A bh (5)(3) 7.5 yd2
2
2
2
1
1
8. A bh (9)(4) 18 m2
2
2
5. A bh (12)(7) 42 cm2
Geometry, Concepts and Skills
Chapter 8 Worked-Out Solution Key
123
Chapter 8 continued
1
1
2
2
1
1
A bh (14)(8) 56 mm2
2
2
1
1
A bh (12)(12) 72 in.2
2
2
1
1
A bh (5)(4) 10 cm2
2
2
1
1
A bh (9)(14) 63 ft2
2
2
They are both right. Sample answer: The sides measuring
15 and 5 can each be a base of the triangle, and 4 and 12
would be their corresponding heights.
9. A bh (7)(4) 14 yd2
10.
11.
12.
13.
14.
1
1
2
2
1
1
(12)(5) (12)(7) (12)(5)
2
2
30 84 30
24. A bh bh bh
144 ft2
1
25. A bh bh
2
1
(8)(6) (8)(5)
2
48 20
68 cm2
3
6
15. Sample answer:
6
12
1
the ratio of the areas is 2 .
2
4
9
12
12
3
16
1
A bh
2
1
22 b(4)
2
44 4b
17.
11 ft b
1
A bh
2
1
63 (14)h
2
126 14h
32
9
the ratio of the areas is 2 .
16
4
1
1
28. A bh (4)(4.8) 9.6 square units
2
2
29.
8 triangles
B
C
A
D
H
E
9 cm h
1
18.
A bh
2
1
80 b(16)
2
160 16b
19.
10 m b
1
A bh
2
1
78 (13)h
2
156 13h
12 in. h
1
20.
A bh
2
1
135 b(9)
2
270 9b
G
F
30. A 8(9.6) 76.8 square units; the octagon is made up
of 8 triangles, each with an area of 9.6 square units. So,
the area of the octagon 8 9.6 76.8 square units.
1
1
2
2
Area of hexagon (number of triangles)(area of one T)
31. Area of triangle bh (9)(7.8) 35.1 in.2
(6)(35.1)
210.6 in.2
32.
c a b
2
2
2
102 62 b2
30 m b
100 36 b2
1
1
2
2
22. Area of rectangular border bh 48(4) 192 in.2;
Number of tiles Area of rectangle Area of triangle
64 b2
21. A bh (4)(2) 4 in.2
8b
1
1
A bh (8)(6) 24 square units
2
2
192 4
48 tiles
1
2
23. A bh bh
1
(7)(4) (7)(4)
2
28 14
42 m2
124
3
4
27. The scale factor of T PQR to T XYZ is ;
4
8
16.
1
2
26. The scale factor of T PQR to T XYZ is ;
Geometry, Concepts and Skills
Chapter 8 Worked-Out Solution Key
33.
c2 a2 b2
262 a2 242
676 a2 576
100 a2
10 a
1
1
A bh (24)(10) 120 square units
2
2
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 8 continued
34.
c2 a2 b2
8.
202 122 b2
400 144 b2
256 b2
16 b
1
1
A bh (16)(12) 96 square units
2
2
1
A bh
2
1
90 (15)h
2
180 15h
1
A bh
2
1
63 b(9)
2
126 9b
9.
12 m h
14 cm b
8.4 Technology Activity (p. 438)
1. The ratios of the areas is the square of the scale factor.
8.4 Standardized Test Practice (p. 437)
2. It stays the same.
a2
then the ratio of their areas is .
b2
4. Answers will vary.
5. Answers will vary, but the area of the triangle will be
9mb
2.72 7.29 larger than the area of the original triangle.
8.4 Mixed Review (p. 437)
Lesson 8.5
1
1
36. x (6 12) (18) 9
2
2
1
1
37. 16 (20 x)
38. 21 (18 x)
2
2
32 20 x
42 18 x
12 x
8.5 Geo-Activity (p. 439)
Step 3. area of parallelogram area of index card; bases are
equal; heights are equal.
Step 4. The area of a parallelogram is the product of the base
and the height.
24 x
8.5 Checkpoint (p. 440)
8.4 Algebra Skills (p. 437)
39. (3, 3)
40. (2, 1)
41. (6, 2)
42. (2, 2)
43. (3, 1)
44. (6, 2)
Quiz 2 (p. 437)
1. A bh (8)(12) 96 yd2
2. A bh (11)(7) 77 mm2
3. A bh (14)(14) 196 ft2
A bh
4.
1. A bh (12)(12) 144 cm2
3. A bh bh
A bh
48 b(6)
8 in. b
Copyright © McDougal Littell Inc.
All rights reserved.
6mb
A bh
6.
28 (7)h
(7)(3) (5)(5)
46 m2
1
1
4. A bh (22)(14) 154 ft2
2
2
1
1
5. A bh (14)(8) 56 mm2
2
2
1
1
6. A bh (16)(12) 96 yd2
2
2
A bh
30 b(5)
6 in. h
(7)(3) (5)(8 3)
21 25
5.
72 (12)h
2. A bh (7)(3) 21 in.2
7.
a
b
3. If two polygons are similar with a scale factor of ,
1
35. B; A bh
2
1
99 (22)h
2
198 22b
4 cm h
8.5 Guided Practice (p. 442)
1.
4
7
2. C
3. A
5. 8 ft, 11 ft
4. B
6. 4 m, 6 m
7. 8 cm, 10 cm
8.5 Practice and Applications (pp. 442–445)
8. A bh (7)(5) 35 square units
9. A bh (11)(6) 66 square units
Geometry, Concepts and Skills
Chapter 8 Worked-Out Solution Key
125
Chapter 8 continued
10. A bh (10)(12) 120 square units
32. A bh bh
11. A bh (3)(2.8) 8.4 square units
(9)(5) (9)(4)
12. A bh (19)(13) 247 square units
45 36
13. A bh (22)(12) 264 square units
14. Agree. Sample answer: Other parallelograms with area
42 ft 2 can be drawn, for example with base 21 feet and
height 2 feet.
15. Area of one g bh (8)(3) 24 cm2
Area of entire piece (number of g )(area of one g )
(8)(24)
192 cm2
16. The base is 4, not 7.
So, the area (4)(5) 20 square units.
1
17. The formula is A bh, not A bh.
2
So, the area (14)(11) 154 square units.
A bh
18.
19.
88 b(8)
30 5h
11 cm b
A bh
20.
39 b(6)
6.5 ft b
A bh
6 in. h
21.
A bh
24.
25.
26.
27.
28.
29.
30.
121 m2
35. A bh (3)(3) 9 square units
36. A bh (2)(3) 6 square units
1
2
1
2
37. A d1d2 (4)(4) 8 square units
38. 152 h2 92
225 h2 81
8mh
144 h2
12 h
132 b(12)
23.
175.5 cm2
1
1
34. A d1d2 bh
2
2
1
1
(12)(16) (5)(10)
2
2
96 25
104 13h
A bh
22.
81 ft2
1
33. A bh bh
2
1
(3)(13) (12)(13)
2
19.5 156
A bh (18)(12) 216 square units
11 ft b
1
1
A d1d2 (16)(13) 104 square units
2
2
1
1
A d1d2 (12)(7) 42 square units
2
2
1
1
A d1d2 (10)(8) 40 square units
2
2
1
1
A d1d2 (14)(10) 70 square units
2
2
1
1
A d1d2 (26)(18) 234 square units
2
2
1
1
A d1d2 (8.1)(12.3) 49.815 square units
2
2
1
1
A d1d2 (15.7)(11.4) 89.49 square units
2
2
1
1
A d1d2 (18.5)(6) 55.5 square units
2
2
39. 262 102 b2
676 100 b2
576 b2
24 b
1
1
A d1d2 (20)(48) 480 square units
2
2
8.5 Standardized Test Practice (p. 445)
40. B; A bh (5)(3) 15 cm2
1
1
41. F; A d1d2 (6)(14) 42 ft2
2
2
1
42. C; A bh bh
2
1
(8)(5) (4)(5)
2
40 10
50 in.2
31. Area of pattern (number of yellow)(area of yellow)
(number of red)(area of red)
(32)(89.49) (21)(55.5)
2863.68 1165.5
8.5 Mixed Review (p. 445)
1
2
43. x (2) 1
4029.18 square units
126
Geometry, Concepts and Skills
Chapter 8 Worked-Out Solution Key
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 8 continued
1
2
36 x 4
44. 18 (x 4)
1
2
2x 16
45. 2x (32)
32 x
46. convex
1
A h(b1 b2)
2
1
294 (14)(30 b2)
2
588 14(30 b2)
7.
x8
47. concave
48. convex
588 420 14b2
168 14b2
8.5 Algebra Skills (p. 445)
12 yd b2
苶2苶 兹4苶苶苶3 兹4苶 兹3苶 2兹3苶
49. 兹1
50. 兹4
苶5苶 兹9苶苶苶5 兹9苶 兹5苶 3兹5苶
8.6 Guided Practice (p. 448)
51. 兹5
苶2苶 兹4苶苶苶3
1苶 兹4苶 兹1苶3苶 2兹1苶3苶
1. Sample answer:
52. 兹8
苶0苶 兹1苶6苶苶苶5 兹1苶6苶 兹5苶 4兹5苶
b1
53. 兹3
苶0苶0苶 兹1苶0苶0苶苶苶3 兹1苶0苶0苶 兹3苶 10兹3
苶
h
54. 兹1
苶2苶5苶 兹2苶5苶苶苶5 兹2苶5苶 兹5苶 5兹5苶
55. 兹1
苶8苶0苶 兹3苶6苶苶苶5 兹3苶6苶 兹5苶 6兹5苶
56. 兹4
苶3苶2苶 兹1苶4苶4苶苶苶3 兹1苶4苶4苶 兹3苶 12兹3
苶
4. 102 62 h2
8.6 Checkpoint (p. 447)
1
2
1
(7)(7 11)
2
1
(7)(18)
2
63 m2
100 36 h2
1
2
1
(14)(16 10)
2
1
(14)(26)
2
182 ft2
2. A h(b1 b2)
1
3. A h(b1 b2)
2
1
(5)(8 12)
2
1
(5)(20)
2
50 cm2
1
4. A h(b1 b2)
2
1
77 h(8 14)
2
1
77 h(22)
2
154 22h
1
A h(b1 b2)
2
1
39 (6)(b1 8)
2
78 6(b1 8)
78 6b1 48
30 6b1
5 cm b1
Copyright © McDougal Littell Inc.
All rights reserved.
64 h2
8 h,
b1 11, b2 6 11 17
5. C
6. A
7. B
8.6 Practice and Applications (pp. 448–450)
1
2
1
(7)(11 15)
2
1
(7)(26)
2
91 square units
1
10. A h(b1 b2)
2
1
(16)(7 24)
2
1
(16)(31)
2
248 square units
1
12. A h(b1 b2)
2
1
(4.6)(6.2 4.4)
2
1
(4.6)(10.6)
2
24.38 square units
8. A h(b1 b2)
7 ft h
5.
2. h 6, b1 7, b2 3 7 5 15
3. h 12, b1 9, b2 19
Lesson 8.6
1. A h(b1 b2)
b2
6.
1
A h(b1 b2)
2
1
84 (8)(13 b2)
2
168 8(13 b2)
168 104 8b2
1
2
1
(8)(6 10)
2
1
(8)(16)
2
64 square units
1
11. A h(b1 b2)
2
1
(14)(13 19)
2
1
(14)(32)
2
224 square units
1
13. A h(b1 b2)
2
1
(15)(14 30)
2
1
(15)(44)
2
330 square units
9. A h(b1 b2)
64 8b2
8 in. b2
Geometry, Concepts and Skills
Chapter 8 Worked-Out Solution Key
127
Chapter 8 continued
14. No. The area is quadrupled:
21.
1
1
(6)(6 9) (6)(15) 45 square units and
2
2
1
1
(12)(12 18) (12)(30) 180 square units;
2
2
4(45) 180
4 units h
15. Sample answer:
3
5
3
7
5
7
5
7
3
The areas are equal.
1
A h(b1 b2)
2
1
(5)(3 7)
2
1
(5)(10)
2
25 square units
16. Answers will vary.
17. Answers will vary; they are the same.
18.
1
A h(b1 b2)
2
1
135 (10)(b1 18)
2
270 10(b1 18)
270 10b1 180
90 10b1
9 cm b1
19.
1
A h(b1 b2)
2
1
132 h(7 17)
2
1
132 h(24)
2
132 12h
11 in. h
20.
1
A h(b1 b2)
2
1
198 (12)(15 b2)
2
396 12(15 b2)
396 180 12b2
216 12b2
18 m b2
128
1
A h(b1 b2)
2
1
50 h(10 15)
2
1
50 h(25)
2
100 25h
Geometry, Concepts and Skills
Chapter 8 Worked-Out Solution Key
22.
1
A h(b1 b2)
2
1
24 (3)(5 b2)
2
48 3(5 b2)
48 15 3b2
33 3b2
11 units b2
1
6
2
12
23. h 13 ft 2 in. 13 ft 13 ft 13.16苶 ft
1
A h(b1 b2)
2
1
(13.16苶)(137 159)
2
1
(13.16苶)(296)
2
1948.6苶
Combined area 2(1948.6苶) ⬇ 3897 ft2
7
12
24. h 13 ft 7 in. 13 ft 13.583
苶 ft
1
1
A bh (21)(13.583苶) ⬇ 142.625 ft2
2
2
Combined area 2(142.625) ⬇ 285 ft2
25. A area of trapezoids area of triangles
3897 285 4182 ft2
1
1
2
2
1
1
(12)(16 30) (12)(16 30)
2
2
1
1
(12)(46) (12)(46)
2
2
276 276
26. A h(b1 b2) h(b1 b2)
552 in.2
1
2
1
(48)(12) (48)(32)
2
288 1536
27. A bh bh
1824 in.2
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 8 continued
1
2
1
(21 16)(9 20) (20)(16)
2
1
(5)(29) (20)(16)
2
72.5 320
28. A h(b1 b2) bh
392.5 in.2
29.
402 h2 242
1600 h2 576
1
2
1
(8)(16 16 6)
2
1
(8)(38)
2
152 ft2
33. H; A h(b1 b2)
8.6 Mixed Review (p. 450)
34. A
35. E
36. C
37. B
38. D
1024 h2
32 h;
1
A h(b1 b2)
2
1
(32)(28 28 24)
2
1
(32)(80)
2
1280 square units
30.
912 h2 352
8281 h2 1225
7056 h2
84 h;
1
A h(b1 b2)
2
1
(84)(100 35 120)
2
1
(84)(255)
2
10,710 square units
31. 172 h2 82
8.6 Algebra Skills (p. 450)
3
5
8
8
8
8
5
2
3
1
40. 9
9
9
3
1
9
1
3
10
5
41. 12
12
12
4
12
6
7
4
1
20
13
42. 35
7
5
35
35
39. 1
Lesson 8.7
8.7 Activity (p. 451)
1. The area of the parallelogram is the product of half the
circumference and the radius.
1
1
2. A C r (2πr) r πr2
2
2
3. A πr2 π(4)2 16π 16(3.14) ⬇ 50.24 square units
8.7 Checkpoint (pp. 453–455)
1. C 2πr
2. C 2πr
289 h2 64
2π(6)
2π(9)
225 h
12π
18π
15 h;
1
A h(b1 b2)
2
1
(15)(25 11 25 8)
2
1
(15)(69)
2
517.5 square units
⬇ 12(3.14)
⬇ 18(3.14)
38 cm
57 ft
2
8.6 Standardized Test Practice (p. 450)
1
32. B; A h(b1 b2)
2
1
(4)(8 13)
2
1
(4)(21)
2
42 in.2
Copyright © McDougal Littell Inc.
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3. C πd
4. A πr2
π(16)
π(8)2
16π
64π
⬇ 16(3.14)
⬇ 64(3.14)
50 in.
201 in.2
5. A πr 2
6. A πr2
π(3)2
π(6)2
9π
36π
⬇ 9(3.14)
⬇ 36(3.14)
28 cm2
113 ft2
x
22
180
360
7. x
28
170 360
8. Geometry, Concepts and Skills
Chapter 8 Worked-Out Solution Key
129
Chapter 8 continued
9. A πr2 π(2)2 4π ⬇ 13 ft2;
14. C πd
x
60
13
360
360x 780
x ⬇ 2 ft2
10. A πr2 π(5)2 25π ⬇ 79 cm2;
x
90
79
360
360x 7110
π(15)
π(4)2
15π
16π
⬇ 15(3.14)
⬇ 50 ft2
47 m
16. A πr2
x ⬇ 20 cm
2
17. A πr2
π(1)2
π(6)2
π
36π
⬇ 3 cm
⬇ 113 in.2
2
11. A πr π(6) 36π ⬇ 113 in. ;
2
15. A πr2
2
2
x
135
113
360
360x 15,255
18. A πr2
19. A πr2
π(9)2
x ⬇ 42 in.
2
π(8)2
81π
64π
⬇ 254 m2
⬇ 201 ft2
20. A πr2
8.7 Guided Practice (p. 455)
1.
21. A πr2
π(9.5)2
π(5.5)2
90.25π
30.25π
⬇ 284 yd
⬇ 95 m2
2
diameter
22. The radius is 6, not 12. The area is 113.04 not 452.16.
radius
23. Sample answer: Disagree. The area of the circle with
radius 5 is about 79. The area of the circle with radius 10
is about 314. Since 314 79 ⬇ 4, the area is quadrupled,
not doubled.
2. Multiply the radius by 2. Then multiply by π by
using the π key on a calculator or by using 3.14 as
an approximation.
Radius, r
Diameter, d
3.
7 in.
14 in.
4.
11 cm
22 cm
5.
3.5 m
7m
6.
0.5 ft
1 ft
24.
A πr2
25.
13 πr2
531 πr2
4.14 ⬇ r2
169.02 ⬇ r2
2 in. r
26.
13 m r
A πr
2
27.
154 πr
49.02 ⬇ r2
8. A πr2 π(3)2
28.
9. A πr2 π(7)2
15.92 ⬇ r2
π(10)
14π
10π
⬇ 14(3.14)
⬇ 10(3.14)
44 cm
31 m
13. C 2πr
2π(2)
2π(13)
4π
26π
⬇ 4(3.14)
⬇ 26(3.14)
13 in.
82 yd
130
A πr
143.88 ⬇ r2
12 units ⬇ r
11. C πd
2π(7)
12. C 2πr
4 units r
2
452 πr2
8.7 Practice and Applications (pp. 456–459)
10. C 2πr
A πr2
50 πr2
2
7 ft r
7. C 2πr 2π(8)
A πr2
Geometry, Concepts and Skills
Chapter 8 Worked-Out Solution Key
d 2r 2(12) 24 units
29.
A πr2
28 πr2
8.91 ⬇ r2
3 units r
d 2r 2(3) 6 units
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 8 continued
30.
A πr2
8.7 Standardized Test Practice (p. 458)
78.5 πr2
40. a. C 2πr
24.99 ⬇ r
2
⬇ 2(3.14)(3960)
5 yd r
24,868.8 mi
C 2πr
C 2πr
b.
2π(5)
24,868.8 10 2πr
10π
24,878.8 2πr
⬇ 31 yd
12,439.4 πr
x
60
31. 12
360
x
100
32. 198
360
33. A πr2
34. A πr2
π(10)
3961.59 mi ⬇ r
c. 3961.59 3960 ⬇ 1.59 mi
π(6)2
2
100π
8.7 Mixed Review (p. 459)
36π
⬇ 314 m ;
x
70
314
360
360x 21,980
41. Exactly one pair of opposite sides are parallel, so the
⬇ 113 ft ;
x
110
113
360
360x 12,430
2
2
x ⬇ 61 m2
x ⬇ 35 ft2
35. A πr2
64π
angles, so it is a rectangle.
43. The quadrilateral has four congruent sides, so it is a
rhombus.
π(15)2
45. A bh 11 8 88 ft2
225π
46. A bh bh
⬇ 707 ft ;
x
145
707
360
360x 102,515
⬇ 201 cm ;
x
45
201
360
360x 9045
2
42. The quadrilateral is a parallelogram with four right
44. A s2 142 196 in.2
36. A πr2
π(8)2
quadrilateral is a trapezoid.
2
x ⬇ 25 cm2
x ⬇ 285 ft2
37. A πr2
(4 2) 4 (6 4) 2
6422
24 4
28 m2
8.7 Algebra Skills (p. 459)
π(12)2
47. 4 7 3
144π
48. 5 (5) 5 5 0
⬇ 452 ft2;
x
145
452
360
360x 65,540
49. (4)(11) 44
50. 12 (12) 12 12 24
51. 33 (3) 11
52. 14 (3) 4 11 4 15
x ⬇ 182 ft2
53. 6 10 16
38. Area of rectangle lw 10 6 60 cm2
Area of circle πr2 π(3)2 9π ⬇ 28 cm2
Area of shaded region Area of rect. Area of circle
60 28
1. A bh (9)(7) 63 ft2
39. Area of rectangle lw 8 4 32 m2
Area of circle πr π(2) 4π ⬇ 13 m
2
55. 22 (9) 22 9 31
Quiz 3 (p. 459)
32 cm2
2
54. (5)(13) 65
2
Area of shaded region Area of rect. 2(area of circle)
2. A bh (5.2)(6.1) 31.72 cm2
1
2
1
2
3. A d1d2 (8)(6) 24 m2
32 2(13)
32 26
6 m2
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Geometry, Concepts and Skills
Chapter 8 Worked-Out Solution Key
131
Chapter 8 continued
1
2
1
(4)(5 4)
2
1
(4)(9)
2
9. Not regular; the polygon is not equilateral and not
4. A h(b1 b2)
equiangular.
10. Regular; the polygon is both equilateral and equiangular.
11. Not regular; the polygon is equiangular but not equilateral.
12. Not regular; the polygon is equilateral but not equiangular.
13. (n 2) 180 (5 2) 180 3 180 540;
18 yd2
5. A πr
121 100 124 104 ma 1 540
6. A πr
2
2
π(3)
449 ma 1 540
π(2)
2
2
9π
ma 1 91
4π
⬇ 28 mm
2
⬇ 13 in.
2
14. (n 2) 180 (6 2) 180 4 180 720;
130 102 120 126 114 ma 1 720
A bh
7.
592 ma 1 720
195 (15)h
ma 1 128
13 cm h
8.
1
A h(b1 b2)
2
1
57 (6)(7 b2)
2
114 6(7 b2)
114 42 6b2
15. 67 90 81 72 ma 1 360
310 ma 1 360
ma 1 50
16. A bh (8)(8) 64 in.
2
17. A bh (12)(6) 72 ft2
18. A bh bh
(7)(5 2) (3)(2)
72 6b2
(7)(3) (3)(2)
12 ft b2
21 6
A πr2
9.
201 πr2
64 ⬇ r2
8 in. r
19.
20.
Chapter 8 Summary and Review (pp. 460–463)
21.
1. A polygon is convex if no line containing a side of the
22.
polygon passes through the interior of the polygon.
2. A polygon is equiangular if all of its interior angles are
23.
congruent.
3. If a polygon is equilateral and equiangular, then it is
regular.
234 9b
4. The amount of surface covered by a figure is its area.
5. The height of a triangle is the perpendicular segment
from a vertex to the line containing the opposite side
of the triangle.
6. Either pair of parallel sides of a parallelogram are called
the bases.
7. A circle is the set of all points in a plane that are the
same distance from a given point.
8. The distance across a circle through its center is the
27 m2
1
1
A bh (11)(8) 44 m2
2
2
1
1
A bh (2)(3) 3 ft2
2
2
1
1
A bh (13)(9) 58.5 cm2
2
2
1
1
A bh (8.5)(11) 46.75 in.2
2
2
1
1
A bh
24.
A bh
2
2
1
1
81 (18)h
117 b(9)
2
2
81 9h
26 ft b
9mh
25. A bh (8)(7) 56 ft2
26. A bh (6)(10) 60 cm2
1
2
A bh
1
2
27. A d1d2 (9)(5) 22.5 in.2
28.
135 (15)h
9 in. h
29.
A bh
121 b(11)
11 m b
diameter.
132
Geometry, Concepts and Skills
Chapter 8 Worked-Out Solution Key
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 8 continued
1
2
1
(7)(6 10)
2
1
(7)(16)
2
31. A h(b1 b2)
56 mm2
1
32. A h(b1 b2)
2
1
(8)(7 11)
2
1
(8)(18)
2
36 ft2
1
33. A h(b1 b2)
2
1
(2)(3 4)
2
1
(2)(7)
2
30. A h(b1 b2)
34.
1
2
1
(6)(4 8)
2
1
(6)(12)
2
72 cm2
1
A h(b1 b2)
2
1
100 h(9 11)
2
1
100 h(20)
2
100 10h
7 m2
10 yd h
35. C 2πr 2π(13) 26π ⬇ 82 in.;
A πr2 π(13)2 169π ⬇ 531 in.2
36. C 2πr 2π(1) 2π ⬇ 6 m;
A πr2 π(4)2 16π ⬇ 50 ft2
38. C πd π(14) ⬇ 44 cm;
A πr2 π(7)2 49π ⬇ 154 cm2
40.
A πr2
50 2πr
380 πr2
25 πr
121 ⬇ r2
8 ft ⬇ r
11 cm r
ma 1 124
6. 50 90 62 65 ma 1 360
267 ma 1 360
ma 1 93
7. A bh (7)(7) 49 ft2
8. A bh (4)(5) 20 cm2
1
1
2
2
10. A bh (8)(13) 104 in.2
1
1
11. A d1d2 (10)(12) 6 mm2
2
2
1
12. A h(b1 b2)
2
1
(6)(9 6)
2
1
(6)(15)
2
45 yd2
9. A bh (7)(4) 14 m2
13. A bh bh
(4)(9) (7 4)(3)
45 m2
1
1
14. A bh h(b1 b2)
2
2
1
1
(5)(3) (4)(5 6)
2
2
1
1
(5)(3) (4)(11)
2
2
7.5 22
29.5 ft2
15. C 2πr 2π(2) 4π ⬇ 13 in.;
Chapter 8 Test (p. 464)
A πr2 π(2)2 4π ⬇ 13 in.2
1–4. Sample answers are given.
1.
596 ma 1 720
36 9
37. C πd π(8) ⬇ 25 ft;
C 2πr
120 111 100 129 136 ma 1 720
(4)(9) (3)(3)
A πr2 π(1)2 π ⬇ 3 m2
39.
5. (n 2) 180 (6 2) 180 4 180 720;
16. C πd π(6) ⬇ 19 m;
2.
A πr2 π(3)2 9π ⬇ 28 m2
17. A πr2 π(5)2 25π ⬇ 79 ft2;
3.
4.
x
130
79
360
360x 10,270
x ⬇ 29 ft2
18. A πr2 π(8)2 64π ⬇ 201 mm2;
x
60
201
360
360x 12,060
x ⬇ 34 mm2
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Geometry, Concepts and Skills
Chapter 8 Worked-Out Solution Key
133
Chapter 8 continued
19. Area of rectangle bh (16)(12) 192 cm2
Area of circle πr2 π(6)2 36π ⬇ 113 cm2
1
2
1
(8)(14)
2
56 m2
6. H; A d1d2
Area of shaded region Area of rect. Area of circle
192 113
79 cm2
1
2
1
(10)(7 13)
2
1
(10)(20)
2
100 yd2
7. A; A h(b1 b2)
1
A bh
2
1
80 b(16)
2
80 8b
20.
10 m b
8. A bh (12)(8) 96 in.2
A bh
21.
9. A πr2 π(4)2 16π ⬇ 50 in.2
104 8h
10. Area of shaded region Area of g Area of circle
13 in. h
22.
96 50
1
A h(b1 b2)
2
1
126 (12)(b1 14)
2
126 6(b1 14)
46 in.2
Chapter 8 Algebra Review
1. 24 2 2 2 2 16
21 b1 14
3. (3) (3) (3) (3) (3) (3) 243
7 ft b1
4. (1)4 (1) (1) (1) (1) 1
A πr2
23.
2. 93 9 9 9 729
5
5. 103 10 10 10 1000
50 πr2
6. 36 3 3 3 3 3 3 729
16 ⬇ r2
7. a p b
4 cm r
Chapter 8 Standardized Test (p. 465)
1. D; (n 2) 180 (7 2) 180 5 180 900
126 118 141 128 121 117 ma C 900
751 ma C 900
ma C 149
2. F; 106 100 2x 90 360
296 2x 360
9.
8. a p b
(60%) 85
(4%) 200
0.6 85
0.04 200
51
8
apb
10.
apb
18 p 40
18
40p
40
40
0.45 p
48 p 300
48
300p
300
300
0.16 p
45% p
16% p
2x 64
x 32
Chapters 7– 8 Project (pp. 468– 469)
3. B; A bh bh
(11)(5) (4)(8 5)
(11)(5) (4)(3)
55 12
67 ft2
1
A bh
2
1
54 b(9)
2
108 9b
4. J;
12 in. b
134
8 in.
1 in.
800 ft
100 ft
1 in.
2. width 200 ft 2 in.,
100 ft
1 in.
length 400 ft 4 in.;
100 ft
A bh (200)(400) 80,000 ft2;
1. scale factor 1
2
5. C; A bh bh
A bh (2)(4) 8 in.2
1
(12)(7) (12)(6)
2
84 36
120 cm2
Geometry, Concepts and Skills
Chapter 8 Worked-Out Solution Key
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 8 continued
3. A bh (2)(2) 4 in.2;
100 ft
length 2 in. 200 ft,
1 in.
100 ft
width 2 in. 200 ft,
1 in.
A bh (200)(200) 40,000 ft2
4. A πr2 π(50)2 2500π ⬇ 2500(3.14) 7850 ft2;
1 in.
50 ft 0.5 in.
100 ft
5.
Actual
Dimensions
Actual
Area
Entire
Park
800 ft 1000 ft
800,000 ft2
8 in. 10 in.
80 in.2
Playing
Field
200 ft 400 ft
80,000 ft2
2 in. 4 in.
8 in.2
Free Run
Meadow
200 ft 200 ft
40,000 ft2
2 in. 2 in.
4 in.2
r 50 ft
7850 ft2
r 0.5 in.
0.79 in.2
Pool
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Dimensions on Area on Scale
Scale Drawing
Drawing
Geometry, Concepts and Skills
Chapter 8 Worked-Out Solution Key
135