Geometry Practice Questions

Use these Geometry practice questions to review triangle rules, circles, perimeter, area, polygons, parallelograms, and the Pythagorean theorem. After answering each question, open the explanation to see the step-by-step solution.

Geometry Topics Covered

  • Special right triangles
  • Circle area and circumference
  • Perimeter of composite figures
  • Triangle angle sums
  • Polygon interior angles
  • Triangle area
  • Parallelogram angle relationships
  • The Pythagorean theorem

Sample Questions

1. In a 30-60-90 triangle, the length of the hypotenuse is 6. What is the length of the shortest side?

  • A. 2
  • B. 3
  • C. 3√2
  • D. 3√3
  • E. 6√2
Show Answer for Question 1
Answer: B. 3
In a 30-60-90 triangle, the side lengths follow this ratio:
1 : √3 : 2
The hypotenuse is the longest side and corresponds to 2 in the ratio. Since the hypotenuse is 6, the shortest side is half of 6.

6 ÷ 2 = 3

Therefore, the shortest side is 3.

2. What is the area of a circle with a diameter of 16?

  • A. 8π
  • B. 16π
  • C. 64π
  • D. 128π
  • E. 256π
Show Answer for Question 2
Answer: C. 64π
The area of a circle is:
A = πr2
The diameter is 16, so the radius is half of 16.

r = 8

Substitute 8 for the radius:

A = π(8)2

A = 64π

3. The figure below contains only horizontal and vertical lines. Calculate its perimeter.

L-shaped polygon. The top horizontal side is labeled 12, the right outer vertical side is labeled 9, the bottom-right horizontal side is labeled 3, and the left outer vertical side is labeled 3. The two inward sides are unlabeled.
  • A. 27
  • B. 33
  • C. 36
  • D. 42
  • E. 48
Show Answer for Question 3
Answer: D. 42
To find the perimeter, add the lengths of all the outside sides.
The missing vertical side is 6, because the full right side is 9 and the left vertical side is 3.
9 − 3 = 6

The missing horizontal side is 9, because the full top side is 12 and the bottom horizontal side is 3.

12 − 3 = 9

Now add the side lengths:

12 + 9 + 3 + 6 + 9 + 3 = 42

The perimeter is 42.

4. Find the measure of the missing angle in the triangle below.

Triangle with an interior angle of 95 degrees at the top vertex and an interior angle of 35 degrees at the lower-right vertex. The lower-left angle is unlabeled.
  • A. 35°
  • B. 40°
  • C. 45°
  • D. 50°
  • E. 55°
Show Answer for Question 4
Answer: D. 50°
The angles inside a triangle add to 180°.
180° − 95° − 35° = 50°
The missing angle is 50°.
5. The circumference of a circle is 30π. What is its area?

  • A. 15π
  • B. 225π
  • C. 400π
  • D. 900π
  • E. 3000π
Show Answer for Question 5
Answer: B. 225π
The circumference of a circle is:
C = 2πr

The circumference is 30π, so substitute 30π for C.

30π = 2πr

Divide both sides by 2π:

r = 15

Now use the area formula:

A = πr2

A = π(15)2

A = 225π

6. What is the sum of the measures of the interior angles of a hexagon?

  • A. 540°
  • B. 720°
  • C. 810°
  • D. 1080°
  • E. 1440°
Show Answer for Question 6
Answer: B. 720°
The sum of the interior angles of a polygon is:
(n − 2) × 180°

A hexagon has 6 sides, so substitute 6 for n.

(6 − 2) × 180° = 4 × 180° = 720°

The sum of the interior angles is 720°.

7. Find the area of the triangle below.

Right triangle with perpendicular legs measuring 8 units horizontally and 5 units vertically.
  • A. 20
  • B. 30
  • C. 35
  • D. 40
  • E. 80
Show Answer for Question 7
Answer: A. 20
The area of a triangle is:

A =

1
2

bh

The base is 8 and the height is 5.

A =

1
2

(8)(5)

A = 20

8. The figure below is a parallelogram with two angles given in terms of x. Determine the value of x.

Parallelogram ABCD with adjacent interior angles. Angle B is labeled 4x plus 12 degrees, and angle C is labeled 3x plus 14 degrees.
  • A. 9
  • B. 10
  • C. 20
  • D. 22
  • E. 24
Show Answer for Question 8
Answer: D. 22
Adjacent angles in a parallelogram are supplementary, which means they add to 180°.
(4x + 12) + (3x + 14) = 180

7x + 26 = 180

7x = 154

x = 22

9. Which of the following could be the side lengths of a right triangle?

  • A. 3, 13, and 14
  • B. 4, 5, and 6
  • C. 4, 9, and 10
  • D. 5, 10, and 15
  • E. 5, 12, and 13
Show Answer for Question 9
Answer: E. 5, 12, and 13
For three lengths to form a right triangle, the square of the longest side must equal the sum of the squares of the other two sides:

a2 + b2 = c2

For 5, 12, and 13:

52 + 122 = 132

25 + 144 = 169

169 = 169

Since the equation is true, 5, 12, and 13 can be the side lengths of a right triangle.

10. The figure below is an equilateral triangle with sides of length 6. What is the area of the triangle?

Equilateral triangle ABC with side length 6. Altitude AX is drawn from the top vertex A perpendicular to base BC.
  • A. 12
  • B. 18
  • C. 36
  • D. 9√3
  • E. 18√3
Show Answer for Question 10
Answer: D. 9√3
An equilateral triangle can be split into two 30-60-90 triangles by drawing a height from the top vertex to the base.

The original side length is 6, so each half of the base is 3.

In a 30-60-90 triangle, the side lengths follow this ratio:

1 : √3 : 2

So the height of the equilateral triangle is 3√3.

Now use the triangle area formula:

A =

1
2

bh

A =

1
2

(6)(3√3)

A = 9√3

How to Use These Geometry Practice Questions

Start by answering each question before opening the explanation. Then compare your work to the step-by-step solution. If you miss a question, review the related geometry rule or formula before moving on.

For extra review, focus on the topics you miss most often. Geometry questions often depend on recognizing the correct formula or relationship, such as triangle angle sums, circle formulas, parallelogram angle rules, or the Pythagorean theorem.

 

Last Updated: July 20, 2026