Geometry and measures worksheet — GCSE Foundation

1.A triangle has vertices X, Y and Z, with a right angle at Y. Side XY is twice as long as side YZ. Which of the following correctly describes this triangle?

2.In one circle, chord PQ is 6 cm long, chord RS is 10 cm long, chord TU is 14 cm long and chord VW is 15 cm long. Write down which of these chords lies closest to the centre of the circle.

3.A triangular prism has two triangular faces and three rectangular faces. How many vertices does a triangular prism have?

4.A kite string makes an angle of 30° with the ground. The kite is flying at a height of 6 m directly above a point on the ground. Using the exact value of sin 30°, work out the exact length of the kite string.

5.The diagram shows a cuboid. Work out the area of its front elevation, in square centimetres.

6.In parallelogram PQRS, angle P = 65°. Which reason correctly explains why angle R = 65°?

7.Here are four trigonometric ratios of special angles. Write down the one that does not have a value.

8.A circle has a radius of 1 cm. Work out the circumference of the circle. Give your answer in terms of π.

9.A garden designer describes a flower bed as a shape with four straight sides: exactly one pair of sides is parallel, those two parallel sides are different lengths, and the other two sides are equal in length to each other but not parallel to each other. Which shape should the designer draw?

10.Two straight lines cross at a point. To find the points that are the same distance from both lines, which construction should be used?

11.A garden water trough is a prism whose cross-section is a right-angled triangle with base 40 cm and height 30 cm. The trough is 120 cm long. Work out the volume of water needed to fill the trough completely.

12.P is the point (3, 4) and Q is the point (6, 0). Work out the distance of each point from the origin, and write down which point is closer to the origin.

13.A sector of a circle has an angle of 90° at the centre. Write down what fraction of the whole circle this sector represents.

14.A builder lays a low wall made from identical bricks. The diagram shows the plan of the wall's footprint on a grid, where each square is one brick. The wall is built up to a height of 4 bricks everywhere. Work out the total number of bricks used.

15.A regular nonagon has 9 sides. Work out the sum of its interior angles.