Geometry and measures worksheet — GCSE Foundation

1.A sector of a circle has radius 4 cm and angle 90°. Using π = 3.14, work out the area of the sector.

2.A sector of a circle has radius 10 cm and angle 72°. Using π = 3.14, work out the arc length of the sector.

3.A goat is tied by a rope 7 m long to a post at a corner of a rectangular field, where two fences meet at a right angle. The goat can reach anywhere inside the field that the rope allows. Using π = 3.14, work out the area the goat can graze, to the nearest square metre.

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

5.The angle between north and a footpath is 35°, measured clockwise from north. What is the three-figure bearing of the footpath?

6.A sector of a circle has angle 120° and an arc length of 31.4 cm. Using π = 3.14, work out the radius of the circle.

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

8.A map has a scale of 1 : 25000. A distance between two points measures 2 cm on the map. What is the real distance, in kilometres?

9.A sector of a circle has radius 6 cm and angle 150°. Using π = 3.14, work out the perimeter of the sector.

10.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.

11.A hiker walks on a bearing of 065°. She then turns clockwise through 90° and continues walking in a straight line. What bearing is she now walking on?

12.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

13.A right-angled triangle has a hypotenuse of 14 cm. One of the other angles is 30°. Work out the exact length of the side opposite the 30° angle.

14.A fish tank is a cuboid measuring 40 cm long, 25 cm wide and 30 cm high. Water is poured in to a depth of 20 cm. Work out the volume of water in the tank, in litres.

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