ExamView - CH 3 Test Review · ID: CH 3 Test Review 14 Say Cheese!: Area and Circumference of a Circle Write the term that best completes each statement. concentric circles diameter

ID: CH 3 Test Review

1

CH 3 Test Review

Boundary Lines: Area of Parallelograms and Triangles

Calculate the area of each figure. Each square on the grid represents a square that is one meter long

and one meter wide.

1. You are making a kite out of nylon fabric. The height of the kite will be 36 inches and the widest part of the

kite will be 24 inches as shown in the diagram. How much nylon fabric will you need to make the kite? Write

the answer in square inches and square feet.

The Keystone Effect: Area of a Trapezoid

Calculate the area of each trapezoid. Each square on the grid represents a square that is one inch long

and one inch wide.

2. The area of a trapezoid is 209 square yards and the bases are 15 yards and 23 yards. What is the height of the

trapezoid?

.

3. The area of a trapezoid is 150 square meters. The height is 10 meters and one base is two meters longer than

the other base. What is each base?


2

Signs, Signs, Every Place There Are Signs!: Area of Regular Polygons

Calculate the area of each regular polygon.

4.

.

5.

.

6. A regular heptagon has a side length of 24 inches and an apothem of 24.9 inches. What is the area of the

regular heptagon?

.

7. A stop sign has a perimeter of 160 inches and an apothem of 24.1 inches. What is the area of the stop sign?

.

8. A regular nonagon has an area of 378 square yards and an apothem of 10.5 yards. What is the length of a side

of the regular nonagon

.


3

9. A regular polygon has an area of 10,080 square meters. The length of a side of the polygon is 30 meters and

the apothem is 56 meters. What type of regular polygon is this?

.

Say Cheese!: Area and Circumference of a Circle

Calculate the circumference and area of each circle. Use 3.14 to approximate π . Each square on the

grid represents a square that is one centimeter long and one centimeter wide.

10. What is the area of the annulus shown? Use 3.14 to approximate π .

.


Define each term in your own words.

11. parallelogram

.

12. altitude of a parallelogram

.


4

13. height of a parallelogram

.

14. altitude of a triangle

.

15. height of a triangle

.

Boundary Lines:Area of Parallelograms and Triangles

Calculate the area of each parallelogram.

EXAMPLE:

A ==== 8(4) ==== 32 mi2

.

16.

.


5

17.

.


In each parallelogram, the base, height, or area is unknown. Calculate the

value of the unknown measure.

EXAMPLE:

A ==== bh

63 ==== 9h

7 ==== h

The height is 7 meters.

.

18.


6


The base of each triangle is labeled. Draw a segment that represents the height of the triangle.

EXAMPLE:

19.

20.


7


Calculate the area of each triangle.

EXAMPLE:

A ====1

2(6)(8) ====

1

2(48) ==== 24 in.

2

.

21.

.

22.


8


In each triangle, the base, height, or area is unknown. Calculate the value of the unknown measure.

EXAMPLE:

A ====1

2bh

30 ====1

2(15)h

60 ==== 15h

4 ==== h

The height of the triangle is 4 meters.

.

23.

.

24.


9


Problem Set

Calculate the area of each trapezoid. Each square on the grid represents a square that is two inches

long and two inches wide.

EXAMPLE:

A =1

2(8 + 16)10 =

1

2(24)(10) = 120

120 square inches

.

25.


10

26.


Calculate the area of each trapezoid with the given dimensions, where h represents the height, b1

represents the length of a base, and b2 represents the length of the other base.

EXAMPLE:

h = 2,b 1 = 4,b 2 = 3

A =1

2(4 + 3)2 =

1

2(7)(2) = 7

The area is 7 square units.

.

27. h = 6, b 1 = 5, b 2 = 3

.

28. h = 5, b 1 = 9, b 2 = 1

.

29. h = 4, b 1 =2

3, b 2 =

4

3


11


In each trapezoid, one base, height, or area is unknown. Calculate the value of the unknown measure.

EXAMPLE:

A =1

2(2 + 4)3 =

1

2(6)(3) = 9

The trapezoid has an area of 9 square feet.

.

30.

.

31.

.


12

32.

.

33.

.

34.


13

Signs, Signs, Every Place There Are Signs!: Area of Regular Polygons

Calculate the area of each regular polygon.

EXAMPLE:

A =1

2(8)(6.3)(6)

A = 151.2

The area is 151.2 square centimeters.

.

35.

.

36.

.

37.


14


Write the term that best completes each statement.

concentric circles diameter radius circle

irrational number circumference annulus

38. The ________________ is the distance around a circle.

39. The distance that is equal to one half the diameter of a circle is the ________________.

40. The distance across a circle through the center is the ________________.

41. A decimal that never repeats or terminates is a(n) _________________.

42. ________________ are circles that share the same center.

43. The ________________ is the region bounded by two concentric circles.


Problem Set: Calculate the diameter of each circle.

EXAMPLE:

d = 2r = 2(6) = 12cm

.

44.


15

45.

.

Say Cheese!:Area and Circumference of a Circle

Calculate the radius of each circle.

r =d

2=

18

2= 9ft

.

46.

.

47.


16


Calculate the circumference of each circle given the radius r of the circle. Write your answers in terms

of π

EXAMPLE:

r = 8 cm

C = 2πr = 2(π)(8) = 16π cm

.

48. r = 2 cm

.

49. r = 10 ft

.

50. r = 4.2 cm

.


Calculate the area of each circle given the radius r of the circle. Write your answers in terms of π .

EXAMPLE:

r = 6 m

A = πr2

= π(62) = 36π m

2

.

51. r = 4 in.


17

52. r = 12 cm

.

53. r = 9.8 yd

.


Calculate the radius of each circle given the circumference C of the circle. Write your answers in terms

of π .

EXAMPLE:

C = 90π mm

C = 2πr

90π = 2πr

45 = r

r = 45 mm

.

54. C = 220π ft

.

55. C = 13π cm

.

56. C = 10.8π mi


18


Calculate the radius of each circle given the area A of the circle. Write your answers in terms of π .

EXAMPLE:

A = 9π cm2

A = πr2

9π = r2

9 = r2

3 = r

r = 3 cm

.

57. A = 16π m2

.

58. A = 49π yd2

.

59. A =1

4π m

2


19


Use the given information to answer each question.

EXAMPLE:

If a circle has a circumference of 6π inches, what is its area?

C = 2πr

6π = 2πr

3 = r

A = πr2

A = π(32)

A = 9π

The area of the circle is 9π square inches.

.

60. If a circle has a circumference of 3π feet, what is its area?

.

61. If a circle has an area of 25π square feet, what is its circumference?


20


Calculate the area of each annulus shown. Use 3.14 to approximate π .

EXAMPLE:

Area of larger circle:

A = πr2

= π(122) = 144π ≈ 452.16 in.

2

Area of smaller circle:

A = πr2

= π(82) = 64π ≈ 200.96 in.

2

Area of annulus:

A ≈ 452.16 − 200.96 = 251.2 in.2

.

62.

.

63.


21

Installing Carpeting and Tile: Area and Perimeter of Composite Figures

Calculate the area of each figure. All measurements are in centimeters. Use 3.14 for π and round

decimal answers to the nearest hundredth.

EXAMPLE:

A = 14(2) + 7(3)

= 28 + 21

= 49 cm2

.

64.

.

65.

.


22

66.

.

Installing Carpeting and Tile: Area and Perimeter of Composite Figures

Calculate the area of the shaded portion of each figure. All measurements are in inches. Use 3.14 for π

and round decimal answers to the nearest hundredth.

EXAMPLE:

A ≈3

4(3.14)(3

2)

=3

4(3.14)(9)

= 21.20 in.2

.

67.


23

68.

.

69.

.

70. All of the line segments in the figure are either vertical or horizontal. Determine the perimeter of the figure.


24

Determine the area of the region bounded by the line segments.

71.

72. All of the line segments in the figure shown are either vertical or horizontal. What is the perimeter of the

figure?

73. All of the line segments in the diagram of the bathroom floor shown are either vertical or horizontal. How

many one-inch square tiles would it take to tile the entire floor?

ID: A

1

CH 3 Test Review

Answer Section

1. ANS:

Area of left triangle =1

2(36)(12) = 216 square inches

Area of right triangle =1

2(36)(12) = 216 square inches

Totalarea of kite = 216 + 216 = 432 square inches

432 square inches ⋅

1 square foot

144 square inches= 3 square feet

You will need 432 square inches, or 3 square feet, of nylon fabric to make the kite.

PTS: 1 REF: Ch3.2 TOP: Assignment

2. ANS:

209 =1

2(15 + 23)h

209 = 19h

11 = h

The height of the trapezoid is 11 yards.


3. ANS:

Let x represent one base. Then x + 2 represents the other base.

150 =1

2(x + x + 2)(10)

150 = 5(2x + 2)

150 = 10x + 10

140 = 10x

14 = x

One base is 14 meters and the other base is 14 + 2 = 16 meters.


4. ANS:

A =1

2(18)(12.4)(5)

= 558 square feet


ID: A

2

5. ANS:

A =1

2(35)(53.9)(10)

= 9432.5 square centimeters


6. ANS:

A =1

2(24)(24.9)(7)

= 2091.6

The area of the regular heptagon is 2091.6 square inches.


7. ANS:

A =1

2(160)(24.1)

= 1928

The area of the stop sign is 1928 square inches.


8. ANS:

378 =1

2(™)(10.5)(9)

378 = 47.25™

8 = ™

The length of a side of the regular nonagon is 8 yards.


9. ANS:

10,080 =1

2(30)(56)(n)

10,080 = 840n

12 = n

The regular polygon has 12 sides. Therefore, the polygon is a regular 12-gon.


ID: A

3

10. ANS:


A = πr2

= π(102) = 100π ≈ 314 m

2


A = πr2

= π(7.52) = 56.25π ≈ 176.625 m

2

Area of annulus:

A ≈ 314 − 176.625 = 137.375 m2

The area of the annulus is approximately 137.375 square meters.


11. ANS:

A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.

PTS: 1 REF: Ch3.2 TOP: Skills Practice

12. ANS:

An altitude of a parallelogram is a line segment drawn from a vertex, perpendicular to the line containing the

opposite side.


13. ANS:

A height of a parallelogram is the perpendicular distance from any point on one side to the line containing the

opposite side.


14. ANS:

An altitude of a triangle is a line segment drawn from a vertex perpendicular to the line containing the

opposite side.


15. ANS:

A height of a triangle is the perpendicular distance from a vertex to the line containing the base of the

triangle.


16. ANS:

A = 11(6) = 66 mi2


17. ANS:

A = 7(16) = 112 yd2


ID: A

4

18. ANS:

A = bh

96 = 12b

8 = b

The base is 8 feet.


19. ANS:


20. ANS:


21. ANS:

A =1

2(7)(7) =

1

2(49) = 24.5 ft

2


ID: A

5

22. ANS:

A =1

2(4.5)(4) =

1

2(18) = 9 m

2


23. ANS:

A =1

2bh

A =1

2(3)(2)

A =1

2(6)

A = 3

The area of the triangle is 3 square feet.


24. ANS:

A =1

2bh

6 =1

2b(3)

12 = 3b

4 = b

The base of the triangle is 4 yards.


25. ANS:

A =1

2(4 + 8)6 =

1

2(12)(6) = 36

36 square inches


26. ANS:

A =1

2(10 + 20)14 =

1

2(30)(14) = 210

210 square inches


ID: A

6

27. ANS:

A =1

2(5 + 3)6 =

1

2(8)(6) = 24



28. ANS:

A =1

2(9 + 1)5 =

1

2(10)(5) = 25



29. ANS:

A =1

2

2

3+

4

3

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃4 =

1

2(2)(4) = 4



30. ANS:

1

2(b 1 + 3)2 = 8

b 1 + 3 = 8

b 1 = 5

The trapezoid has a base of 5 centimeters.


31. ANS:

1

2(b 1 + 8)5 = 25

b 1 + 8 = 10

b 1 = 2

The trapezoid has a base of 2 yards.


32. ANS:

1

2(5 + 15)h = 70

10h = 70

h = 7

The trapezoid has a height of 7 yards.


ID: A

7

33. ANS:

A =1

2(13 + 22)5 =

1

2(35)(5) = 87.5

The trapezoid has an area of 87.5 square feet.


34. ANS:

1

2(b 1 + 13)7 = 98

b 1 + 13 = 28

b 1 = 15

The trapezoid has a base of 15 meters.


35. ANS:

A =1

2(12)(8.3)(5)

= 249

The area is 249 square feet.


36. ANS:

A =1

2(10)(10.4)(7)

= 364

The area is 364 square yards.


37. ANS:

A =1

2(4)(7.5)(12)

= 180

The area is 180 square inches.


38. ANS: circumference


39. ANS: radius


40. ANS: diameter


ID: A

8

41. ANS: irrational number


42. ANS: concentric circles


43. ANS: annulus


44. ANS:

d = 2r = 2(22) = 44ft


45. ANS:

d = 2r = 2(9.75) = 19.5 in.


46. ANS:

r =d

2=

100

2= 50m


47. ANS:

r =d

2=

10.5

2= 5.25 yd


48. ANS:

C = 2πr = 2(π)(2) = 4π cm


49. ANS:

C = 2πr = 2(π)(10) = 20π ft


50. ANS:

C = 2πr = 2(π)(4.2) = 8.4π cm


51. ANS:

A = πr2

= π(42) = 16π in.

2


52. ANS:

A = πr2

= π(122) = 144π cm

2


ID: A

9

53. ANS:

A = πr2

= π(9.82) = 96.04π yd

2


54. ANS:

C = 2πr

220π = 2πr

110 = r

r = 110 ft


55. ANS:

C = 2πr

13π = 2πr

6.5 = r

r = 6.5 cm


56. ANS:

C = 2πr

10.8π = 2πr

5.4 = r

r = 5.4 mi


57. ANS:

A = πr2

16π = πr2

16 = r2

4 = r

r = 4 m


ID: A

10

58. ANS:

A = πr2

49π = πr2

49 = r2

7 = r

r = 7 yd


59. ANS:

A = πr2

1

4π = πr

2

1

4= r

2

1

2= r

r =1

2m


60. ANS:

C = 2πr

3π = 2πr

1.5 = r

A = πr2

A = π(1.52)

A = 2.25π

The area of the circle is 2.25π square feet.


61. ANS:

A = πr2

25π = πr2

25 = r2

5 = r

C = 2πr

C = 2π(5)

C = 10π

The circumference of the circle is 10π feet.


ID: A

11

62. ANS:


A = πr2

= π(222) = 484π ≈ 1519.76 ft

2


A = πr2

= π(112) = 121π ≈ 379.94 ft

2

Area of annulus:

A ≈ 1519.76 − 379.94 = 1139.82 ft2


63. ANS:


A = πr2

= π(342) = 1156π ≈ 3629.84 m

2


A = πr2

= π(27.22) = 739.84π ≈ 2323.10 m

2

Area of annulus:

A ≈ 3629.84 − 2323.10 = 1306.74 m2


64. ANS:

A =1

2(30 + 15)(15) +

1

2(20)(15)

= 337.5 + 150

= 487.5 cm2


65. ANS:

A = 21

2

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃(1)(2) + 4(1)

= 2 + 4

= 6 cm2


66. ANS:

A =1

2(6)(4) +

1

2(5)(10)

= 12 + 25

= 37 cm2


ID: A

12

67. ANS:

A ≈ 8(5) −1

2(3.14)(2.5

2)

= 40 − 9.8125

= 30.19 in.2


68. ANS:

A =3

4

1

2(32)(27.7)

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

=3

4(443.2)

= 332.4 in.2


69. ANS:

A ≈ 20(20) − (3.14)(102)

= 400 − 314

= 86 in.2


70. ANS:

The perimeter is 12 + 12 + 8 + 8 = 40 centimeters.

PTS: 1 REF: Ch3.6 TOP: Mid Ch Test

71. ANS:

To determine the area, you can add the areas of the two rectangles. One rectangle is 11 units by 12 units and

the other rectangle is 10 units by 6 units.

Total area = 11(12) + 10(6) = 132 + 60 = 192

The area of the region bounded by the line segments is 192 square units.

PTS: 1 REF: Ch3.6 TOP: End Ch Test

72. ANS:

The sum of the shorter horizontal segments is 20 yards, and the sum of the shorter vertical segments is 18

yards. So, 20 + 20 + 18 + 18 = 76.

The perimeter is 76 yards.


ID: A

13

73. ANS:

First, calculate the sum of the areas of the two rectangles:7(6) + 5(9) = 42 + 45 = 89 square feet. Then,

multiply the number of square feet by 144, the number of square inches in one square foot:

89 × 144 = 12,816.

So, 12,816 one-inch square tiles are needed to tile the entire floor.


Documents

ExamView - CH 3 Test Review · ID: CH 3 Test Review 14 Say Cheese!: Area and Circumference of a Circle Write the term that best completes each statement. concentric circles diameter