Basic Geometry Practice Questions with Full Answer Key – Area, Perimeter, Volume & Angles

High School geometry questions similar to what you will find on a standardized test.

Geometry Practice Test

1. What is measurement of the indicated angle assuming the figure is a square?

a. 45 o
b. 90 o
c. 60 o
d. 30 o

2. What is the sum of all the angles in the rectangle above?

a. 180 o
b. 360 o
c. 90 o
d. 120 o

3. What is the measurement of the indicated angle?

a. 45 o
b. 90 o
c. 60 o
d. 50 o

4. If the line m is parallel to the side AB of ?ABC, what is angle a?

a. 130 o
b. 25 o
c. 65 o
d. 50 o

5. What is perimeter of the above shape?

a. 12 cm
b. 16 cm
c. 6 cm
d. 20 cm

6. What is (area of large circle) – (area of small circle) in the figure above?

a. 8 п cm 2
b. 10 п cm 2
c. 12 п cm 2
d. 16 п cm 2

7. What is perimeter of ?ABC in the above shape?

8. What is the volume of the figure above?

a. 125 cm 3
b. 875 cm 3
c. 1000 cm 3
d. 500 cm 3

9. What is the volume of the above solid made by a hollow cylinder with half in size of the larger cylinder?

a. 1440 п in 3
b. 1260 п in 3
c. 1040 п in 3
d. 960 п in 3

Answer Key

1. B
The diagonals of a square intersect perpendicularly with each other so each angle measures 90 o
x =90 o

2. B
a+b+c+d = ?
The sum of angles around a point is 360 o a+b+c+d = 360 o

Video Solution

3. C
The sum of angles around a point is 360 o
d+300 = 360 o
d = 60 o

Video Solution

4. D
Two parallel lines(m & side AB) intersected by side AC
a= 50 o (interior angles)

5. B
The square with 2 cm side common to the rectangle apart from 4cm side
Perimeter = 2+2+2+4+2+4 = 16 cm

6. C
In the figure, we are given a large circle and a small circle inside it;
with the diameter equal to the radius of the large one. The diameter of the
small circle is 4 cm. This means that its radius is 2 cm. Since the diameter
of the small circle is the radius of the large circle, the radius of the large
circle is 4 cm. The area of a circle is calculated by: пr 2 where r is the
radius. Area of the small circle: п(2) 2 = 4п Area of the large circle: п(4) 2 2 = 16п

The difference area is found by:
Area of the large circle – Area of the small circle = 16п – 4п = 12п

7. D
Perimeter of a shape with two squares and triangle ABC.
Perimeter = 8.5+8.5+6+6
Perimeter = 29 cm.

8. C
Large cube is made up of 8 smaller cubes of 5 cm sides.
Volume = Volume of small cube x 8
Volume = (5 x 5 x 5) x 8, 125 x 8
Volume = 1000cm 3

9. B
Volume= Volume of large cylinder – Volume of small cylinder
(Volume of cylinder = area of base x height)
We know the small cylinder is 1/2 the size of the large cylinder
So, Volume of the small cylinder
= Large Cylinder (п 12 2 x 10) – Small Cylinder(п 6 2 x 5)
= 1440п – 180п
Volume of small cylinder = 1260п in 3

Most Popular Geometry Questions

Common geometry questions on on standardized tests :

• Solve for the missing angle or side
• Finding the area or perimeter of different shapes (e.g. triangles, rectangles, circles)
• Problems using the Pythagorean Theorem
• Calculate properties of geometric shapes such as angles, right angles or parallel sides
• Calculating volume or surface area of complex shapes for example spheres, cylinders or cones
• Solve geometric transformations such as rotation, translation or reflections

Most Common Geometry Mistakes on a Test

1. Not clearly labeling or identifying the given and unknown information in a problem
2. Not understanding the properties and definitions of basic geometric figures (e.g. line, angle, triangle, etc.)
3. Incorrectly using basic formulas (e.g. area of a triangle, Pythagorean theorem)
4. Incorrectly interpreting geometric diagrams
5. Not understanding the relationship between parallel lines and transversals
6. Not understanding the relationship between angles and their degree measures
7. Not understanding the relationship between perimeter and area

Written by, Brian Stocker MA., Complete Test Preparation Inc.

Date Published: Thursday, April 3rd, 2014
Date Modified: Tuesday, June 18th, 2024