Geometry Pre-AP
Review: Area and Perimeter
Name: ___________________________
Date: _____________Period:________
Find the area and perimeter of each polygon. For each problem: write formula, substitution, then
solve. Answers for problems involving 45-45-90, 30-60-90, or Pythagorean Theorem should be in
simplest radical form.
1.
2.
9 2
3
12
54
3.
6
45
3
6
60
6
4.
5.
60
6.
45
60
3
3
9
12
10
30
3
7.
23
8.
5
21
5
9.
5
11
5
4
6
13
For each word problem you must draw a figure.
10. The length of a rectangle is 12 more than its width. Find the area of the rectangle if its perimeter is
100cm.
11. A path 2m wide surrounds a rectangular garden 20m long and 12m wide. Find the area of the path.
12. A room 28ft long and 20ft wide has walls 8ft high.
a. What is the total wall area?
b. How many gallon cans of paint should be bought to paint the walls if 1 gallon of paint covers 300ft2?
13. A wooden fence 6ft high and 220ft long is to be painted on both sides.
a. What is the total area to be painted?
b. A gallon of a certain type of paint will cover only 200ft2 of area for the first coat, but on the second
coat a gallon of the same paint will cover 300ft2. If the fence is to be given two coats of paint, how
many gallons of paint should be bought?
14. A rectangle having an area of 392m2 is twice as long as it is wide. Find its dimensions.
15. The lengths of the sides of three squares are s, s+1, and s+2. If their total area is 365cm2, find their total
perimeter.
16. The area of a rhombus is 100. Find the length of the two diagonals if one is twice as long as the other.
17. The base of a triangle is 1cm longer than its altitude. If the area of the triangle is 210cm2, how long is
the altitude?
18. A rectangular table is 76cm wide. If its area is 8664cm2, find its length.
19. Find the area of a rectangle with a base length of 15m and a diagonal length of 17m.
20. Find the area of a rectangle if the length of a base is 5in and the length of a diagonal is 13in.
21. The area of a rectangle is 28cm2 and its perimeter is 22cm. Find the dimensions of the rectangle.
22. The area of a rectangle is 75in2 and the length is 3 times the width. Find the length and the width.
23. The legs of an isosceles trapezoid are 10cm. The bases are 9cm and 21cm. Find the area of the
trapezoid and the lengths of the diagonals.
24. An isosceles trapezoid has bases 12 and 28. The area is 300. Find the height and the perimeter.
25. Find the area of an isosceles trapezoid with bases 8 and 18 and 45 base angles.
26. Find the area of an isosceles trapezoid with legs 10 and bases 10 and 22.
27. Find the area of a rhombus with diagonals 4 and 6.
28. Find the area of an equilateral triangle with sides of 8ft.
29. Find the area of an isosceles triangle with base 10 and perimeter 36.
30. Find the area of a parallelogram with a 45 angle and sides 6 and 10.
31. Find the area of rhombus QRST if mQSR=50 and the length of the shorter diagonal is 6.
32. Find the length of a side of a square that has an area equal to that of a rhombus with diagonals 9 and 8.
33. Find the area of a regular pentagon inscribed in a circle with a radius of 5.
34. Find the area of a regular hexagon circumscribed about a circle with a radius of 6.
35. Find the area of a regular octagon with side lengths of 2.
36. If the area of an equilateral triangle is 100 3 cm2, find the length of a side.
37. The area of a regular hexagon is 54 3 , find the apothem and length of each side.
38. Find the area of an isosceles triangle with a 32 vertex angle and a base of 8cm.
39. One base of a trapezoid is twice the other. The height is equal to the longer base and the area is 60.
Find the height of the trapezoid.
40. Find the area of an isosceles trapezoid with 45 base angles and bases 8 and 14.
41. Two similar triangles have corresponding sides with lengths 8 and 4. If the area of the smaller triangle is
52, what is the area of the larger triangle?
42. The area of a rectangle is 16 times that of a similar one. Find the ratio of corresponding side lengths.
43. Two similar triangles have heights of 6 cm and 9cm. If the perimeter of the smaller triangle is 28, find
the perimeter of the larger triangle.
44. Two similar trapezoids have heights of 4 cm and 6 cm. The area of the smaller trapezoid is 35 cm².
Find the area of the larger trapezoid.
45. Two similar parallelograms have an area of 8 ft² and 18 ft². If the smaller parallelogram has a side
length of 8 ft., what is the side length of the larger parallelogram?
46. The ratio between the perimeters of two squares is
4
. Find the area of the larger square if the area of
10
the smaller square is 84 in².
47. The ratio between the circumferences of two circles is
4
. Find the area of the smaller circle if the area
7
of the larger one is 147 cm².
48. If the area of a circle is 196π in², find the circumference.
Find the area of the shaded region.
21
49.
50.
4
r=3 for all circles
51.
52.
16
d = 14
Find the area of each polygon with the given vertices.
53. A(9,9), B(4,-4), C(-2,-4)
54. X(2,1), Y(5,3), Z(7,1)
55. L(7,5), M(5,0), N(3,5), P(5,10)
56. T(-4,4), U(5,3), V(5,-5), W(-4,-1)
57. The area of a given triangle is 9 times that of a similar triangle. Find the ratio of the lengths of the
corresponding sides of the two triangles.
58. The area of a rectangle is 16 times that of a similar one. Find the ratio of corresponding side lengths.
59. The length of each side of a triangle is doubled. What is the effect on the perimeter? What is the effect
on the area?
60. The lengths of the sides of a square are tripled. What is the effect on the perimeter? On the area?
61. Two similar triangles have corresponding sides with lengths 8 and 4. If the area of the smaller triangle is
52, what is the area of the larger triangle?
62. A sign painter is copying a corporate symbol. The area of a triangle on the letterhead logo is 30 mm2 and
the length of the side is 6 mm. The length of the corresponding side of the triangle on the sign logo is
75cm. What is the area of the triangle on the sign?
63. Given ABC is similar to DEF with AB = 18 in and corresponding side DE = 3in, and the area of
 ABC = 72in2. Find the area of  DEF.
Estimate the area of the irregular Shapes.
64. A = _________
66.
65. A = _________
Probability = _________
67. Probability = _________
68. Probability = _________
5
4
Find the probability of throwing a sticky ball into the shaded region.
69.
70.
6 ft
10 ft
7 ft
A point is chosen randomly in ACEF. Find the probability of each event. Round to the nearest
hundredth.
4 cm
F
71. The point is in BDG.
72. The point is in circle H.
H
G 45
°
73. The point is in the shaded region.
E
45
°
A
B
D
C
Find the probability that a point chosen randomly inside the rectangle is inside each shape. Round to
the nearest hundredth.
74. The regular hexagon
6m
75. The triangle
76. The circle or the triangle
24 m
8m
10 m
40 m