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Geometry
Chapter 11 Review
Name ______________________________
Period ______
For numbers 1 – 3, find the value of x.
1.
2.
145
97
125
117
x
88
3.
 3x
 4x+5
 5x
 x-15
 2x+10
4. The measure of each interior angle of a regular polygon is 108 . How many sides
does the polygon have?
5. A convex heptagon has interior angles that measure
101,145,137,153,139 and 108 . What is the measure of the seventh interior angle?
6. What is the sum of the measures of the interior angles of a convex 25-gon?
7. What is the measure of an exterior angle if the regular polygon has 15 sides?
8. A convex octagon has exterior angles that measure 50,82, 45, 27, 25,14 and 64 .
What is the measure of the exterior angle of the eight vertex?
9. Find the area of the triangle.
10. Find the area or the regular pentagon.
11. Find the perimeter of the regular
hexagon.
12. Find the area the perimeter of a square
With a diagonal of 12 inches.
13. A hexagon has one side length of 25 inches. Another similar hexagon has a
corresponding side length of 10 inches. Find the ratio of the perimeters of the smaller to
the larger hexagon.
14. A regular octagon has a perimeter of 125 in and an area of 32.5 in 2 . Find the
perimeter of a similar octagon with an area of 292.5 in 2 .
15. The ratio of the lengths of two squares is 5:11. What is the ratio of their areas?
16. A regular pentagon has an area of 169 cm 2 . Find the scale factor of this pentagon to
a similar pentagon with an area of 225 cm 2 .
17. Find the circumference of a circle with a diameter of 11 in. Round to the nearest
hundredth.
18. Find the radius of a circle with a circumference of 50 m. Round to the nearest
hundredth.
19. Find the length of AB . Round to the nearest tenth.
20. Find the radius of
Q. Round to the nearest tenth.
21. Find the radius of a circle with an area of 755 cm 2 .
22. Find the area of a circle with a diameter of 17 in. Round to the nearest hundredth.
23. Find the circumference of a circle whose area is 85 m 2 . Round to the nearest tenth.
24. Find the area of the sector shown in the diagram. Round to the nearest tenth.
25. Find the radius of
C , if AB  67 and the area of the shaded region is 28.65 cm 2 .
26. A birthday cake is cut into 12 equal pieces. If the cake has a diameter of 10 inches,
what is the area of one piece of cake? Round to the nearest hundredth.
27. Find the probability that a point chosen at random in the regular triangle lands in the
shaded region.
8
28. Find the probability that a point chosen at random lands in the shaded region. Round
to the nearest tenth.
14
25
29. Find the probability that a point chosen at random in the circle lands in the shaded
region. Round to the nearest tenth.
30. Find the circumference of
Q.
For numbers 31 & 32, use the diagram to answer.
31. Find the probability that a point chosen at random on AE is on BD .
32. Find the probability that a point chosen at random on BE is on CD .
33. What is the area of a regular pentagon if its apothem has a length of 3 feet and each
side has a length of 7.7 feet?
34. Find the length of the apothem of a square if the area of the square is 100 m 2 .
35. What is the sum of the exterior angles in a convex 13-sided polygon?
36. What is the area of the shaded region in the diagram?
37. What is the measure of one exterior angle in a regular 9-sided polygon?
38. What is the circumference of a circle with a radius of 5.7 inches?
39. What is the value of x?
40. A regular hexagon has sides of length of 6 ft. Another regular hexagon has sides of
length 10 ft. Find the ratio of the area of the larger hexagon to the area of the smaller
hexagon.
KEY
1. 97 
21. 15.5 cm
2. 32 
22. 226.98 in 2
3. x = 24
23. 32.7 m
4. n = 5
24. 52.4 in 2
5. 117 
25. 7 cm
6. 4140
26. 6.54 in 2
7. 24 
27. 25%
8. 53 
28. 60.7%
9. 10.83 square units
29. 44.4%
10. 363.3
30. 90 in
11. 72 units
31. 50%
12. A = 72 in 2 P = 34 in
32. .43
13. 2:5
33. 57.8 ft 2
14. 375 in
34. 5 m
15. 25:121
35. 360 
16. 13:15
36. 41.1
17. 34.56 in
37. 40 
18. 7.96 m
38. 35.8 in
19. 9.4 cm
39. 40 
20. 8.1 cm
40. 25:9