ACT Prep Area of Polygons
1.
In the figure below, F and E are points on GD . What is the ratio of the area of
square ABEF to the area of the parallelogram ACDG ?
A. 1:14
B. 1:7
C. 7:1
D. 7:2
E. 2:7
2.
In the figure below, a square is circumscribed about a circle with a 30-inch diameter.
Points A, B, C, and D are the midpoints of the square’s sides. What is the total area,
in square inches, of the shaded regions?
F. 450
G. 225
H. 177
J. 94
K. 47
3.
You have enough material to build a fence 40 meters long. If you use it all to
enclose a square region, how many square meters will you enclose?
A. 160
B. 100
C. 80
D. 40
E. 20
4.
The area of the trapezoid below is 16 square inches, the altitude is 2 inches, and the
length of one base is 3 inches. What is the length, b, of the other base, in inches?
A. 2 23
B. 5
C. 11
D. 13
E. 15
5.
If the rectangle and the right triangle in the figure below have the same area, and
indicated lengths are given in inches, what is x expressed in terms of a ?
F. a
G. a
3
2
H. a 3
J. a 5
K. a 6
6.
What is the area, in square inches, of the figure shown below?
F. 18
G. 30
H. 36
J. 44
K. 60
7.
How many square feet is the area of the shaded triangle below?
A. 15
B. 18
C. 20
D. 24
E. 30
8.
In the diagram below, AED and BCD each measure 135, DF is an altitude of
CDE and ABCE is a rectangle. What is the area, in square meters, of pentagon
ABCDE ?
A. 28 + 8 2
B. 96
C. 112
D. 120
E. 140
9.
Below, in right triangle ABC, AB is 4 inches long and BC is 5 inches long. What
is the area, in square inches, of square ACDE ?
F. 9
G. 41
H. 82
J. 4 41
K. 41
10. Each side of a certain cube is a square with an area of 64 square inches. What is the
volume of the cube, in cubic inches?
F. 264
G. 218
H. 212
J. 29
K. 23
11. The following sketch shows a living room wall from the front. What is the area of the
front surface of this wall, in square feet?
A. 26
B. 64
C. 72
D. 80
E. 640
12. In the figure below, with side lengths given in inches, C and D are right
angles. What is the total area of pentagon ABCDE, in square inches.
F.
G.
H.
J.
K.
48
60
60.5
63
72
13. A certain rectangle is 3 times as long as it is wide. Suppose the length and width are
both doubled. The area of the second rectangle is how many times as large as the
area of the first?
A. 2
B. 3
C. 4
D. 6
E. 12
14. In the parallelogram below, lengths are given in centimeters. What is the area of the
parallelogram, in square centimeters?
A. 4
B. 8
C. 17
D. 34
E. 2 17
15. Given the vertices of parallelogram ABCD in the standard (x,y) coordinate plane
below,
what is the area of ABC, in square units?
A. 10.5
B. 21.0
C. 42.0
D. 45.0
E. 90.0
16. If all angles in the figure shown below are right angles and each dimension given is in
inches, then what is the area of the figure, in square inches?
A.
B.
C.
D.
E.
35
44
62
83
96
17. The dimensions of parallelogram ABCD, shown below, are given in centimeters.
What is the area, in square centimeters, of parallelogram ABCD ?
F.
G.
H.
J.
K.
25
36
40
50
80
18. The length of one side of a square is increased by 25%. By what percent would the
length of the adjacent side have to be decreased so that the area of the new figure
(which will be rectangular) is the same as the area of the original square?
F.
G.
H.
J.
20%
25%
50%
75%
19. In the figure below, ABCD is a square. Points are chosen on each pair of adjacent
sides of ABCD to form 4 congruent right triangles, as shown below. Each of these
has one leg that is twice as long as the other leg. What fraction of the area of square
ABCD is shaded?
A.
B.
C.
D.
E.
1
9
2
9
4
9
5
9
8
9