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Ch 10 Review
Possible exam questions for the chapter 10 exam
1. Find the area. The figure is not drawn to scale.
A. B. C. D.
0% 0%0%0%
25 in.
40 in.47 in.
A. 1175 in2
B. 1000 in2
C. 65 in2
D. 130 in2
10-1
1. Find the area. The figure is not drawn to scale. 25 in.
40 in.47 in.
10-1
Area of a parallelogram is base times height.
The correct answer is B. 1000 in2.
2. Find the area. The figure is not drawn to scale.
A. B. C. D.
0% 0%0%0%
5 cm
6.7 cm
A. 11.7 cm2
B. 33.5 cm2
C. 16.75 cm2
D. 67 cm2
10-1
2. Find the area. The figure is not drawn to scale.
5 cm
6.7 cm
10-1
Area of a triangle is base times height divided by 2.
The correct answer is C. 16.75 cm2
3. The area of a parallelogram is 100 cm2 and the height is 25 cm. Find the corresponding base.
A. B. C. D.
0% 0%0%0%
A. 125 cmB. 75 cmC. 4 cmD. 2,500 cm2
10-1
3. The area of a parallelogram is 100 cm2 and the height is 25 cm. Find the corresponding base.
10-1
Area of a parallelogram is base times height.
The correct answer is C. 4 cm
A. 38.5 cm2
B. 105 cm2
C. 87.5 cm2
D. 11 cm2
4. Find the area of the trapezoid. Leave your answer in simplest radical form.
A. B. C. D.
0% 0%0%0%
7 cm
7 cm
4 cm
45°
Not drawn to scale10-2
4. Find the area of the trapezoid. Leave your answer in simplest radical form. 7 cm
7 cm
4 cm
45°
Not drawn to scale
10-2
Area of a trapezoid is half the height times the sum of the bases.
The correct answer is C. 87.5cm2
5. Find the area of the trapezoid. Leave your answer in simplest radical form.
A. B. C. D.
0% 0%0%0%
60°
4 ft
17 ft
Not drawn to scale
A. ft2
B. ft2
C. ft2
D. ft2
10-2
5. Find the area of the trapezoid. Leave your answer in simplest radical form.
60°
4 ft
17 ft
Not drawn to scale
10-2
Area of a trapezoid is half the height times the sum of the bases.
The correct answer is A.
6. What is the area of the kite?
A. B. C. D.
25% 25%25%25%
3 3
168
ft ft
ftft A. 72 ft2
B. 144 ft2
C. 60 ft2
D. 15 ft2
10-2
6. What is the area of the kite?
3 3
168
ft ft
ftft
10-2
Area of a kite is half of diagonal one times diagonal two.
The correct answer is A. 72 ft2
7. Given a regular octagon, find the measures of the angles formed by (a) two consecutive radii and (b) a radius and a side of the polygon.
A. B. C. D.
25% 25%25%25%
A. 72°; 252°B. 45°; 67.5°C. 36°; 216°D. 40°; 230°
10-3
7. Given a regular octagon, find the measures of the angles formed by (a) two consecutive radii and (b) a radius and a side of the polygon.
10-3
a) 360 divided by 8 gives the angle at the center
b) Angle formed between a side and a radius is an acute angle in a right triangle. Add half of part (a) to 90 and subtract from 180
Correct answer is B. 45°; 67.5°
8. Find the area of a regular hexagon with an apothem 17.3 centimeters long and a side 20 centimeters long. Round your answer to the nearest tenth.
A. B. C. D.
25% 25%25%25%
A. 173.2 cm2
B. 2078.5 cm2
C. 692.8 cm2
D. 1038 cm2
10-3
8. Find the area of a regular hexagon with an apothem 17.3 centimeters long and a side 20 centimeters long. Round your answer to the nearest tenth.
10-3
The formula for the area of a polygon is
The correct answer is D. 1038 cm2
9. Find the area of a regular hexagon with side length of 10 m. Round your answer to the nearest tenth.
A. B. C. D.
25% 25%25%25%
A. 450 m2
B. 259.8 m2
C. 129.9 m2
D. 86.6 m2
9. Find the area of a regular hexagon with side length of 10 m. Round your answer to the nearest tenth.
The formula for the area of a polygon is The perimeter is 6 * 10 = 60
To find the apothem you need special right triangles.The apothem is the long leg of a 30-60-90 triangle. The short leg is 5 so the long leg is
The correct answer is B. 259.8 m2
10. 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.
A. B. C. D.
25% 25%25%25%
A. 5 : 6 and 36 : 49B. 6 : 7 and 25 : 36C. 5 : 6 and 25 : 36D. 6 : 7 and 36 : 49
10-3
15 cm
18 cm
10. 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.
10-3
15 cm
18 cm
The ratio is the ratio of the side lengths.
The ratio of the perimeters is the same.
The ratio of their areas is
Correct answer is C. 5 : 6 and 25 : 36
8 m 60 m
Not drawn to scale
11. The trapezoids are similar. The area of the smaller trapezoid is 53 m . Find the area of the larger trapezoid to the nearest whole number.
A. B. C. D.
25% 25%25%25%10-4
A. 64 m2
B. 3600 m2
C. 70 m2
D. 2981 m2
8 m 60 m
Not drawn to scale
11. The trapezoids are similar. The area of the smaller trapezoid is 53 m . Find the area of the larger trapezoid to the nearest whole number.
10-4
Find by comparing side lengths
Square them to find
Set up the proportion and cross multiply and divide.
Correct answer is D. 2981
12. Find the area of the regular polygon. Give the answer to the nearest tenth.pentagon with a side of 5 ft
A. B. C. D.
0% 0%0%0%
10-5
A. 34.4 ft2
B. 43 ft2
C. 86 ft2
D. 8.6 ft2
12. Find the area of the regular polygon. Give the answer to the nearest tenth.pentagon with a side of 5 ft
10-5
5 ft
The area of a polygon is
The perimeter is 5 * 5 = 25
The apothem is found using trigonometry.
The central angle is or 72 degreesThat makes the top angle of the triangle 36 degrees
So the apothem is found using trigonometry:
=
The correct answer is B. 43 ft2
2.5 ft
a
10 cm
9 cm
13. Find the area of the triangle. Give the answer to the nearest tenth. The drawing may not be to scale.
A. B. C. D.
38%
8%
21%
33%
10-5
A. 43.5 cm2
B. 86.9 cm2
C. 167.9 cm2
D. 11.6 cm2
10 cm
9 cm
13. Find the area of the triangle. Give the answer to the nearest tenth. The drawing may not be to scale.
10-5
The area of a triangle given two sides and an included angle is as follows:
Correct answer is A 43.5 cm2
14. What are the minor arcs of ?
A. B. C. D.
25%
50%
17%
8%
10-6
H K
L
J
O
H K
L
J
O
14. What are the minor arcs of ?10-6
Minor arcs are less than 180 degrees. So there are 4 minor arcs:
Correct answer is D.
15. Find the circumference. Leave your answer in terms of .
A. B. C. D.
8%
33%
42%
17%
10-6
18 in.
A. 324 in.B. 54 in.C. 36 in.D. 18 in.
15. Find the circumference. Leave your answer in terms of .
10-6
18 in.
Circumference is twice pi times the radius.
Correct answer is C.
16. Find the length of . Leave your answer in terms of .
A. B. C. D.
0%
21%
13%
67%10-6
12 m
X
Y
P
A. 1080 mB. 36 mC. 6 mD. 18 m
16. Find the length of . Leave your answer in terms of .
10-6
12 m
X
Y
P
Arc length is a percentage of the circumference.
Correct answer is D.
17. Find the area of the circle. Leave your answer in terms of .
A. B. C. D.
25% 25%
42%
8%
10-7
4.6 m
A. 12.2 m2
B. 21.16 m2
C. 10.58 m2
D. 5.29 m2
17. Find the area of the circle. Leave your answer in terms of .
10-7
4.6 m
Area of a circle is pi times radius squared.
The correct answer is D. .
18. Find the exact area of the shaded region.
A. B. C. D.
25% 25%25%25%10-7
A
OB
14 ft
A. (49 - 98) ft2
B. (49 - 196) ft2
C. (49 - 98) ft2
D. None of these
Area of a segment is the area of the sector – the area of the triangle.
Correct answer is A. (49 - 98) ft2
A
OB
14 ft
18. Find the exact area of the shaded region. 10-7
19. Find the probability that a point chosen at random from is on the segment .
A. B. C. D.
42% 42%
4%
13%
10-8
J
0
K L M N O P Q R S T
1 2 3 4 5 6 7 8 9 10
A. B. C. D.
19. Find the probability that a point chosen at random from is on the segment .
10-8
J
0
K L M N O P Q R S T
1 2 3 4 5 6 7 8 9 10
Correct answer is A.
20. Lenny’s favorite radio station has this hourly schedule: news 20 min, commercials 3 min, music 37 min. If Lenny chooses a time of day at random to turn on the radio to his favorite station, what is the probability that he will hear the news?
A. B. C. D.
71%
4%4%
21%
10-8
A. B. C. D.
20. Lenny’s favorite radio station has this hourly schedule: news 20 min, commercials 3 min, music 37 min. If Lenny chooses a time of day at random to turn on the radio to his favorite station, what is the probability that he will hear the news?
10-8
Correct answer is A.
Ch 10 Formulas
