Chapter 10 Practice Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Find the area. The figure is not drawn to scale.
____
1.
7.6 cm
3.7 cm
a.
____
b.
c.
d.
c. 138 in.2
d. 1440 in.2
b. 5.4 cm2
c. 21.6 cm2
d. 7.4 cm2
b. 6.5 yd2
c. 13 yd2
d. 15 yd2
2.
36 in.
40 in.
33 in.
a. 1188 in.2
____
b. 69 in.2
3.
2 cm
5.4 cm
a. 10.8 cm2
____
4.
3 yd
10 yd
a. 30 yd2
____
5.
9 cm
8 cm
13 cm
9 cm
____
____
11 cm
a. 144.5 cm2
b. 127 cm2
c. 172 cm2
d. 50 cm2
a. 188 in.2
b. 278 in.2
c. 322 in.2
d. none of these
c. 303.66 in.2
d. 77.2 in.2
c. 75 in.2
d. 70 in.2
6.
7.
19 in.
12.6 in.
14.5 in.
29.2 in.
a. 607.32 in.2
____
b. 36.7 in.2
8.
8 in.
7 in.
8 in.
12 in.
Not drawn to scale
a. 77.2 in.2
____
b. 80 in.2
9. The area of a parallelogram is 420 cm2 and the height is 35 cm. Find the corresponding base.
a. 385 cm
b. 455 cm
c. 14,700 cm2
d. 12 cm
Find the area of the trapezoid. Leave your answer in simplest radical form.
____ 10.
8 ft
10 ft
60°
Not drawn to scale
a. 40
b. 16
ft2
ft2
c. 24
ft2
d. 32
____ 11. Find the area of the rhombus.
8m
8m
8m
8m
a. 12 m2
b. 4096 m2
c. 128 m2
d. 32 m2
____ 12. Find the area of the rhombus. Leave your answer in simplest radical form.
60°
5
Not drawn to scale
a. 50
b. 10 3
c. 25 6
____ 13. Given the regular hexagon, find the measure of each numbered angle.
d. 50 3
ft2
3
1
2
a.
b.
c.
d.
____ 14. Find the area of a regular hexagon with an apothem 10.4 yards long and a side 12 yards long. Round your
answer to the nearest tenth.
a. 748.2 yd2
b. 374.4 yd2
c. 62.4 yd2
d. 249.4 yd2
____ 15. Find the area of a regular hexagon with side length of 8 m. Round your answer to the nearest tenth.
a. 55.4 m2
b. 166.3 m2
c. 83.1 m2
d. 288 m2
____ 16. Find the area of an equilateral triangle with side 12.
a. 36
b. 72
c. 36
d. 3
____ 17. Find the area of the regular polygon. Round your answer to the nearest tenth.
13.07 in.
10 in.
2
a. 176.6 in.
b. 966.1 in.2
c. 80.0 in.2
d. 483.0 in.2
____ 18. Find the area of an equilateral triangle with radius 8
m. Leave your answer in simplest radical form.
2
2
a. 96
b.
c.
d. 12
m
m
m2
m2
144
18
The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to
the second. The figures are not drawn to scale.
____ 19.
15 yd
40 yd
a.
b.
and
and
c.
and
d.
and
____ 20.
15
18
a. 5 : 6 and 25 : 36
b. 6 : 7 and 36 : 49
c. 5 : 6 and 36 : 49
d. 6 : 7 and 25 : 36
____ 21. The widths of two similar rectangles are 16 cm and 14 cm. What is the ratio of the perimeters? Of the areas?
a. 8 : 7 and 64 : 49
c. 9 : 8 and 81 : 64
b. 9 : 8 and 64 : 49
d. 8 : 7 and 81 : 64
The figures are similar. The area of one figure is given. Find the area of the other figure to the nearest
whole number.
____ 22. The area of the larger triangle is 1589 ft .
40 ft
35 ft
Not drawn to scale
a. 1217 ft
b. 1225 ft
____ 23. The area of the smaller trapezoid is 558 m .
c. 1600 ft
d. 2075 ft
24 m
57 m
Not drawn to scale
a. 3147 m
b. 3249 m
c. 576 m
d. 14 m
____ 24. It costs a family $324 to buy a 10-ft-by-12-ft rug. At this rate, what will it cost them to buy a 15-ft-by-18-ft
rug?
a. $729
b. $270
c. $388.80
d. $466.56
____ 25. Grade 7 students were surveyed to determine how many hours a day they spent on various activities. The
results are shown in the circle graph below. Find the measure of each central angle in the circle graph.
a. Sleeping
b. Eating
a. 118.8°; 28.8°
b. 108°; 28.8°
c. 118.8°; 288°
d. 59.4°; 288°
c. arc ADB; 245°
d. arc AB; 245°
____ 26. Name the minor arc and find its measure.
A
D
C
) 115°
B
a. arc ADB; 30°
b. arc AB; 115°
____ 27. Name the major arc and find its measure.
A
D
) 50°
C
B
a. arc ADB; 50
b. arc AB; 50
c. arc ADB; 310
d. arc AB; 310
____ 28. Identify a semicircle that contains C.
C
A
B
0
a. semicircle ABC
b. semicircle AC
c. semicircle CB
d. semicircle ACB
Find the circumference. Leave your answer in terms of
.
____ 29.
5.7 cm
a.
cm
b.
cm
c.
cm
d.
cm
d.
in.
____ 30.
18 in.
a.
in.
b.
in.
c.
in.
____ 31. Find the length of arc XPY. Leave your answer in terms of
.
X
8m
Y
P
a. 24
m
b. 12
m
c. 4
m
d. 720
Find the area of the circle. Leave your answer in terms of
m
.
____ 32.
3.6 m
a. 25.92
m2
b. 1.8
m2
c. 12.96
m2
d. 46.66
c. 16.81
m2
d. 11.2
m2
____ 33.
4.1 m
a. 4.2025
m2
b. 8.405
m2
m2
____ 34. Find the area of the figure to the nearest tenth.
105°
9
a. 74.2 in.2
b. 8.2 in.2
____ 35. Find the exact area of the shaded region.
c. 148.4 in.2
d. 23.6 in.2
a.
c.
b.
d. none of these
Short Answer
36. The regular polygon has radius 9 m. Find each angle measure to the nearest tenth of a degree, each linear
measure to the nearest tenth of a meter, and the square measure to the nearest square meter.
G
H
F
A
X
O
E
B
D
a.
b.
c.
d.
e.
f.
C
OX
AB
the perimeter
the area
Essay
37.
a.
b.
Find the area of a regular hexagon with sides 2 cm long. Leave your answer in simplest
radical form.
Use your answer from part (a) to find the area of a regular hexagon of side length 8.
Other
38. Write an explanation that justifies the statement: The area of a regular polygon is half the product of the
apothem and the perimeter.
Chapter 10 Practice Test
Answer Section
MULTIPLE CHOICE
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24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
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A
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A
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B
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D
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A
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B
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C
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D
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C
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D
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C
STA:
10-3 Example 1
B
STA:
10-3 Example 2
B
STA:
10-3 Example 3
A
STA:
10-3 Example 3
D
STA:
10-3 Example 3
B
STA:
10-3 Example 4
D
STA:
A
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A
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A
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A
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A
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C
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D
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CA GEOM 8.0| CA GEOM 10.0
TOP: 10-1 Example 1
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TOP: 10-1 Example 1
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CA GEOM 8.0| CA GEOM 10.0| CA GEOM 20.0
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CA GEOM 8.0| CA GEOM 10.0| CA GEOM 20.0
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CA GEOM 11.0
CA GEOM 11.0
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CA GEOM 7.0| CA GEOM 8.0
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CA GEOM 7.0| CA GEOM 8.0
CA GEOM 8.0
CA GEOM 8.0
CA GEOM 8.0
CA GEOM 8.0
TOP:
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10-4 Example 1
10-4 Example 1
10-4 Example 1
10-4 Example 2
10-4 Example 2
10-4 Example 3
10-6 Example 1
10-6 Example 3
10-6 Example 3
10-6 Example 2
10-6 Example 4
10-6 Example 4
10-6 Example 5
10-7 Example 1
10-7 Example 1
10-7 Example 2
10-7 Example 3
SHORT ANSWER
36. ANS:
a. 22.5
b. 45
c. 8.3 m
d. 6.9 m
e. 55.2 m
f. 229 m
STA: CA GEOM 8.0| CA GEOM 19.0
ESSAY
37. ANS:
[4] Answers may vary. Sample:
a.
The central angle of one of the triangles in the hexagon is
altitude of the triangle is

because it is a
-
-
. The
right triangle.
2 cm

1 cm
The area of the hexagon is therefore
b.
Because regular hexagons are similar, their areas will be proportional to the
square of their similarity ratio.
[3]
[2]
[1]
correct methods but with a minor computational error
error in method
correct answer but with no work shown
STA: CA GEOM 11.0
OTHER
.
.
cm2.
38. ANS:
Answers many vary. Sample: The apothem of a regular polygon is the height of one of n equal triangles into
which the figure is divided. So, each triangle’s area is
. But sn is the perimeter, so the total area is
, where s is the length of a side. The total area is
.
STA: CA GEOM 8.0| CA GEOM 10.0| CA GEOM 20.0
TOP: 10-3 Example 2