Geometry and measures worksheet — GCSE Higher

1.A shop stacks identical storage crates in a display. The diagram shows the plan of the floor positions used, with one corner position marked. Every floor position is filled with crates stacked 3 high, except the marked corner position, which is left completely empty. Work out how many crates are used in total.

2.A zip wire is fixed at an angle of 50° to the horizontal, running from a high platform down to the ground. The zip wire itself, from the platform to the ground, is 12 m long. Work out the horizontal distance covered by the zip wire. Give your answer correct to 1 decimal place.

3.A triangular solar panel has two edges of length 1.8 m and 1.3 m, with an angle of 72° between them. Manufacturing the panel costs £85 per square metre. Work out the total manufacturing cost. Give your answer to the nearest penny.

4.A parallelogram has an area of 84 cm² and a base of 12 cm. Work out the perpendicular height of the parallelogram.

5.A sector of a circle has radius 6 cm and an area of 4.71 cm². Using π = 3.14, work out the angle of the sector.

6.A support strut for a shed roof is in the shape of a right-angled triangle. The two shorter sides of the strut are 5 m and 9 m. Work out the length of the sloping strut (the hypotenuse). Give your answer correct to 1 decimal place.

7.Two cylindrical storage tins are geometrically similar. The smaller tin has height 4 cm and the larger tin has height 6 cm. Work out the ratio of the surface area of the smaller tin to the surface area of the larger tin, giving your answer in the form a : b in its simplest form.

8.A shop sells rice in packs of 250 g. Aisha buys 4 packs. Work out the total mass of rice she buys, in kilograms.

9.Two similar ponds have perimeters in the ratio 4 : 11. The perimeter of the larger pond is 88 m. Work out the perimeter of the smaller pond.

10.A trapezium-shaped garden bed has parallel sides of 2.5 m and 4.5 m, and a perpendicular width of 3 m. A gardener wants to know the area of the bed before ordering topsoil. Work out the area of the garden bed.

11.In triangle ABC, AB = 11 cm, AC = 9 cm and the area of the triangle is 45 cm². Given that angle BAC is obtuse, work out the size of angle BAC. Give your answer to 1 decimal place.

12.A surveyor is marking out field ABCD for a new crop. The plan states that side AB is parallel to side DC, but AB and DC are not equal in length, and sides BC and AD are not parallel to each other. Which term correctly describes the shape of field ABCD?

13.In triangle ABC, AB = 8 cm, BC = 11 cm and AC = 6 cm. Work out the size of angle ABC. Give your answer to 1 decimal place.

14.Sam says: '3.2 litres is the same as 320 ml, because you multiply by 100.' Which statement about Sam's claim is correct?

15.A scale drawing shows a room that is 5 cm wide. The real room is 15 m wide. Write the scale of the drawing in the form 1 : n.