Free GCSE Geometry Practice Test: Area, Angles, Pythagoras, Trig

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

16 cm² 30 cm² 60 cm² 36 cm²

Answer: Area = ½ × base × height = ½ × 10 × 6 = 30 cm².

2. What is the circumference of a circle with diameter 10 cm?

5π cm 10π cm 20π cm 25π cm

Answer: Circumference = π × diameter = 10π cm.

3. The exterior angles of any polygon add up to …

180° 360° 540° It depends on the sides

Answer: Walking around any polygon you make one full turn, so exterior angles total 360°.

4. What is each interior angle of a regular hexagon?

60° 108° 120° 135°

Answer: Each exterior angle is 360° ÷ 6 = 60°, so each interior angle is 180° − 60° = 120°.

5. What is the volume of a cuboid measuring 3 cm by 4 cm by 5 cm?

12 cm³ 47 cm³ 60 cm³ 94 cm³

Answer: Volume = length × width × height = 3 × 4 × 5 = 60 cm³.

6. sin 30° =

0 1/2 √3/2 1

Answer: sin 30° = 1/2, one of the exact values worth memorising.

7. Alternate angles on parallel lines are …

equal add up to 180° add up to 90° always right angles

Answer: Alternate (Z) angles are equal; co-interior angles add to 180°.

8. A right-angled triangle has shorter sides of 5 cm and 12 cm. How long is the hypotenuse?

13 cm 17 cm 60 cm 7 cm

Answer: 5² + 12² = 25 + 144 = 169, and √169 = 13 cm.

9. What is the three-figure bearing of due east?

000° 090° 180° 270°

Answer: Bearings are measured clockwise from north; east is a quarter turn: 090°.

10. A trapezium has parallel sides of 4 cm and 8 cm and a height of 5 cm. What is its area?

30 cm² 60 cm² 40 cm² 20 cm²

Answer: Area = ½(a + b)h = ½ × 12 × 5 = 30 cm².

About this test

Geometry questions reward knowing a handful of facts and formulae cold. Most mistakes come from mixing up radius and diameter, or interior and exterior angles; these questions target exactly those.

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