Geometry and measures worksheet — GCSE Foundation

1.A triangular flag has a base of 40 cm and a perpendicular height of 25 cm. Work out its area.

2.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.

3.A quadrilateral has angles of 100°, 85° and 95° at three of its vertices. Work out the fourth angle.

4.A sector of a circle has radius 12 cm and angle 45°. Using π = 3.14, work out the area of the sector.

5.A ship's radar shows a lighthouse at the point (12, −4) on a grid measured in nautical miles. The ship is at (2, 5). The ship sails along the vector that takes it directly to the lighthouse, then sails along that same vector again. Work out the ship's final position.

6.A composite solid is made from a cylinder of radius 3 cm and height 10 cm, with a cone of the same radius and vertical height 4 cm fixed on top, apex upward. Work out the total volume of the solid. Use π = 3.14 and give your answer correct to 1 decimal place.

7.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.

8.A photograph is 10 cm wide and 15 cm tall. It is enlarged to make a similar poster that is 40 cm wide. The poster costs £0.80 per centimetre of its height to print, based on its full height. Work out the cost of printing the poster.

9.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.

10.A quadrilateral has both pairs of opposite sides parallel and equal in length, but none of its angles are right angles. Which statement about this quadrilateral is correct?

11.A right-angled triangle has a hypotenuse of 10 cm. One of its other angles is 45°. Work out the exact length of one of the two shorter sides.

12.A shop stacks tins in a display block. The front elevation of the block is 4 tins wide and 3 tins high. The side elevation shows the block is 2 tins deep. Every position in the block is filled. How many tins are used in total?

13.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.

14.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.

15.The angle between north and a cycle path is 40°, but it is measured anticlockwise from north. What is the three-figure bearing of the cycle path?