Geometry and measures worksheet — GCSE Foundation

1.Write down the exact value of sin 60°.

2.A sprinkler waters a sector-shaped patch of a garden with radius 8 m and angle 90°. Work out the perimeter of the watered sector, to 1 decimal place. (Use π = 3.14.)

3.A bus journey takes 2.5 hours. Work out how many minutes this is.

4.Loose sweets are sold at £1.20 per 100 g. Work out the cost of 350 g of sweets.

5.A ladder of length 7 m leans against a vertical wall. The foot of the ladder is 3 m from the base of the wall. Work out how high up the wall the ladder reaches. Give your answer correct to 1 decimal place.

6.A rectangle has vertices A(0, 0), B(6, 0), C(6, 4) and D(0, 4). Work out the length of the diagonal AC. Give your answer correct to 2 decimal places.

7.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.

8.Two straight lines PQ and RS cross at point O. Angle POR = 52°. Work out angle QOS.

9.A cylinder has a volume of 942 cm³ and a height of 12 cm. Using π = 3.14, work out the radius of the cylinder.

10.A footpath sign shows a distance of 0.45 km to the next village. Work out this distance in metres.

11.A cake recipe takes 135 minutes from start to finish. Write this time as hours and minutes.

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

13.A gardener wants to buy edging trim to go all the way around a circular flower bed with a diameter of 8 m. Work out the length of edging trim needed, using π = 3.14. Give your answer to the nearest metre.

14.Two vertical masts stand on level ground, 40 m apart. One mast is 30 m tall and the other is 50 m tall. Work out the straight-line distance between the tops of the two masts. Give your answer to 1 decimal place.

15.A room measures 4.2 m by 3.6 m. A flooring company needs the area in cm² to order the right amount of vinyl flooring. Work out the area of the room in cm².