Geometry Practice Test
1. The perimeter of the isosceles triangle drawn below is 150 cm and the altitude h = 45 cm ,
How many square centimeters are in its area? The image is not drawn to scale.
a. 1080
b. 2160
c. 135
d. 90
e. 4320
2. Each corner of an inner square bisects the side of its outer square. If the area of the biggest
square is 512 cm2, how many square centimeters are in the area of the smallest square? The image
is not drawn to scale.
a. 17
b. 18
c. 13
d. 19
e. 16
3. In the picture below, we have AC = AB = 13 cm. and BC = 10 cm. The green circle is
inscribed in the isosceles triangle ABC. How many square centimeters are in the area of the
triangle COB? Give your answer to the nearest tenth. The image is not drawn to scale.
a. 1.9
b. 12.0
c. 60.0
d. 16.7
e. 23.1
4. The vertices of a rectangle ABCD are A = (4,4), B = (44,4), C = (44,13), and D = (13,4) . How
long is diagonal AC?
a. 40
b. 39
c. 41
d. 44
e. 38
5. In the picture below, we have CA = CB, CM = CN and the angle ACM = 40° . How many
degrees are in the measure of the angle NMB? The picture is not drawn to scale.
a. 40
b. 20
c. 18
d. 38
e. 22
6. The coordinates of the vertices of the triangle ABC are
A = (58, 37), B = (10, 8) and C = (16, 18) . What is the length of the median AM ? The image is
not drawn to scale.
a. 50
b. 49
c. 54
d. 51
e. 48
7. What is the length of the median to the hypotenuse of a right triangle if the hypotenuse has
length 12 ?
a. 3
b. 6
c. 12
d. 3
e. 9
8. The quadrilateral MNPQ and the circle inscribed in it are pictured below. In addition, we have
QP = 9 and MN = 18 . What is the perimeter of the quadrilateral MNPQ? The image is not drawn
to scale.
a. 27
b. 56
c. 51
d. 57
e. 54
9. The triangle pictured below is an isosceles triangle such that BC = 30 cm long. If the area of
the triangle cannot exceed 540 square centimeters, what is the maximum number of centimeters
in the perimeter of the triangle?
a. 107
b. 106
c. 108
d. 111
e. 105
10. A chord MP of the larger circle of two concentric circles is tangent to the smaller circle at N
and measures 16 inches. What is the number of square inches in the area between the two circles?
The answer is x π . Find x .
a. 65
b. 66
c. 61
d. 67
e. 64
11. Find the area of the trapezoid pictured below
if a = 11, b = 14 and h = 18 .
a. 225
b. 224
c. 223
d. 228
e. 222
12. The total surface area of a rectangular box
is given by one of the following expression:
a. 2(a + b)h + 2ab
b. (a + b)h + 2ab
c. 2(a + b)h + ab
d. (a + b)h + ab
e. 2(a + b)h - 2ab
13. Suppose ABC is a right triangle in B and AMN is a right triangle in M. (See the picture
below). This of course implies that BC is parallel to MN. Suppose that AC= 212, AB= 112 and
BM= 56 . Find the area of the trapezoid BCNM? The picture below is not drawn to scale.
a. 12610
b. 12620
c. 12600
d. 12570
e. 12630
14. Let ABC be a right isosceles triangle with hypotenuse AC=16 units long. Let P be the
midpoint of AC and consider the circle of diameter BP . Find the area of the region inside the
circle but outside the triangle ABC ? The answer is one of the following
Which one ?
a. 8 (π - 1) square units
b. 8 (π - 2) square units
c. 4 (π - 2) square units
d. 8 (2 π -3) square units
e. 4 (π - 1) square units
15. In the picture below, the segment PC is a diameter of the circle and O is its center. The line
MCN is tangent to the circle at the point C. If n = 22 degrees. How many degrees are in the
measure of s ? The picture is not drawn to scale and not all parts of that picture are necessary to
solve this problem.
a. 22
b. 44
c. 68
d. 66
e. 46
16. In the picture below, the segment PC is a diameter of the circle and O is its center. The line
MCN is tangent to the circle at the point C . Suppose that n = 20 degrees. How many degrees are
in the measure of q ? The picture is not drawn to scale and not all parts of that picture are
necessary to solve this problem.
a. 140
b. 80
c. 78
d. 72
e. 70
17. In the picture below we have that MNQ and MPC are secants to the circle. The points P,N,Q
and C are on the circle. Suppose that MP = 4 units, PC = 8 units and NQ = 2 units . How many
units are in the length of MN ? The picture is not drawn to scale.
a. 7
b. 8
c. 6
d. 3
e. 9
18. In the figure below, we have AB is parallel to DC and the measure of the angle ADC is 45
degrees. We also have AH = BG = 70 cm, CD = 135 cm and AB = 41 cm . if AH and BG are
perpendicular to CD , what is the number of centimeters in the length of line segment BC ? The
picture is not drawn to scale.
a. 73
b. 74
c. 72
d. 77
e. 71
19. In the figure below, we have AB is parallel to DC and the measure of the angle ADC is 45
degrees. We also have CD = 142 cm and AB = 48 cm. If AH and BG are perpendicular to CD and
the area of the trapezoid ABCD is 6650 cm2, what is the number of square centimeters in the area
of the rectangle ABGH? The picture is not drawn to scale.
a. 3290
b. 3220
c. 3570
d. 3150
e. 3360
20. Consider a right triangle ABC that is rectangle in A as in the picture below: The small letters
in the pictures above denote the length of the corresponding segments and AH is the height
corresponding to the hypotenuse. If b = 35 units and c = 12 units, how many units are in the
length of a ? The picture is not drawn to scale and you might not need all parts of the picture
below to answer the question asked.
a. 36
b. 35
c. 40
d. 37
e. 34