Geometry Quiz

Geometry studies shapes, sizes and the properties of space. This quiz covers angles, triangles, circles, area, perimeter and volume with exam-style questions.

What this quiz covers

Study tip: Draw a quick diagram for every question; many wrong answers come from imagining the figure incorrectly.

Questions, answers and explanations

1. How many degrees are there in a right angle?

  1. 45°
  2. 90°
  3. 180°
  4. 360°

Answer: 90°

A right angle always measures 90 degrees.

2. What is the sum of the interior angles of a triangle?

  1. 90°
  2. 180°
  3. 270°
  4. 360°

Answer: 180°

The sum of the interior angles of every triangle is 180°.

3. How many sides does a hexagon have?

  1. 5
  2. 6
  3. 7
  4. 8

Answer: 6

A hexagon is a polygon with 6 sides.

4. Which shape has all sides equal and all angles equal?

  1. Rectangle
  2. Square
  3. Parallelogram
  4. Trapezium

Answer: Square

A square has four equal sides and four equal 90° angles.

5. What is the perimeter of a square with side length 5 cm?

  1. 10 cm
  2. 15 cm
  3. 20 cm
  4. 25 cm

Answer: 20 cm

Perimeter of a square = 4 × side = 4 × 5 = 20 cm.

6. How many sides does an octagon have?

  1. 6
  2. 7
  3. 8
  4. 9

Answer: 8

An octagon is a polygon with 8 sides.

7. What is the area of a rectangle with length 8 cm and width 5 cm?

  1. 13 cm²
  2. 26 cm²
  3. 40 cm²
  4. 80 cm²

Answer: 40 cm²

Area = Length × Width = 8 × 5 = 40 cm².

8. A straight angle measures:

  1. 90°
  2. 120°
  3. 180°
  4. 360°

Answer: 180°

A straight angle is exactly 180 degrees.

9. How many diagonals does a square have?

  1. 1
  2. 2
  3. 3
  4. 4

Answer: 2

A square has two equal diagonals.

10. What is the circumference formula of a circle?

  1. πr²
  2. 2πr
  3. πd²
  4. r²

Answer: 2πr

The circumference of a circle is C = 2πr.

11. What is the area of a triangle with base 10 cm and height 6 cm?

  1. 30 cm²
  2. 60 cm²
  3. 16 cm²
  4. 20 cm²

Answer: 30 cm²

Area of a triangle = ½ × base × height = ½ × 10 × 6 = 30 cm².

12. How many sides does a pentagon have?

  1. 4
  2. 5
  3. 6
  4. 7

Answer: 5

A pentagon is a polygon with 5 sides.

13. What is the value of π (pi) approximately?

  1. 2.14
  2. 3.14
  3. 4.13
  4. 3.41

Answer: 3.14

The approximate value of π is 3.14.

14. A triangle with all three equal sides is called:

  1. Scalene Triangle
  2. Isosceles Triangle
  3. Equilateral Triangle
  4. Right Triangle

Answer: Equilateral Triangle

An equilateral triangle has all three sides equal.

15. What is the sum of the angles in a quadrilateral?

  1. 180°
  2. 270°
  3. 360°
  4. 540°

Answer: 360°

The interior angles of any quadrilateral always add up to 360°.

16. What is the perimeter of a rectangle with length 8 cm and width 4 cm?

  1. 24 cm
  2. 32 cm
  3. 20 cm
  4. 16 cm

Answer: 24 cm

Perimeter = 2 × (Length + Width) = 2 × (8 + 4) = 24 cm.

17. A circle has a radius of 7 cm. What is its diameter?

  1. 7 cm
  2. 10 cm
  3. 12 cm
  4. 14 cm

Answer: 14 cm

Diameter = 2 × Radius = 2 × 7 = 14 cm.

18. Which angle is greater than 90° but less than 180°?

  1. Acute Angle
  2. Right Angle
  3. Obtuse Angle
  4. Straight Angle

Answer: Obtuse Angle

An obtuse angle measures more than 90° and less than 180°.

19. How many vertices does a cube have?

  1. 6
  2. 8
  3. 10
  4. 12

Answer: 8

A cube has 8 vertices (corners).

20. Which theorem is used to find the hypotenuse of a right triangle?

  1. Newton's Theorem
  2. Pythagoras Theorem
  3. Binomial Theorem
  4. Euclid's Division Lemma

Answer: Pythagoras Theorem

Pythagoras Theorem states: a² + b² = c².

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