Geometry and measures worksheet — GCSE Foundation

1.A scale drawing of a park uses a scale of 1 : 2000. A path is drawn 8.5 cm long on the drawing. A cyclist rides the length of the path and then rides straight back again along the same path. How far does the cyclist travel in total, in metres?

2.A square has sides of length 7 cm. Work out its area.

3.Two similar signs have lengths in the ratio 9 : 4. The larger sign has a side of length 14.4 cm. Work out the length of the corresponding side of the smaller sign.

4.In a right-angled triangle one of the other two angles is 45°, and the side opposite that 45° angle is 7 cm. Work out the length of the hypotenuse. Give your answer to 1 decimal place.

5.A fan-shaped rug is in the shape of a sector of a circle with radius 4 m and angle 180°. It costs £4 per square metre to make. Using π = 3.14, work out the total cost of the rug.

6.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.

7.The bearing of a campsite B from a walker's position A is 070°. What is the bearing of A from B?

8.Write down the term for the distance all the way around the edge of a circle.

9.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.

10.A sector of a circle has radius 9 cm and angle 120°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.

11.Two angles lie on a straight line. One angle is 37°. Work out the size of the other angle.

12.A water tank is a cube with edges of length 2 m. Work out how many cubic centimetres the tank holds when it is full.

13.A cuboid-shaped shipping crate has a length of 12 m, a width of 5 m, and a volume of 360 m³. Work out the height of the crate, in metres.

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

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