Geometry and measures worksheet — GCSE Higher

1.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.

2.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?

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

4.A footpath is 3750 m long. Work out this distance in kilometres.

5.Two hikers walk from a campsite A to a lookout B, a distance of 14 km on a bearing of 038°. From B they walk to a shelter C, a distance of 20 km on a bearing of 142°. Work out the direct distance from A to C. Give your answer to 1 decimal place.

6.A garden flower bed is in the shape of a trapezium. Its two parallel edges are 3.5 m and 6.5 m long, and the perpendicular distance between them is 4 m. Bedding plants cost £2.50 per square metre to cover the bed. Work out the total cost of the bedding plants.

7.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?

8.In triangle ABC, AB = AC = 9 cm and angle ABC = angle ACB = 65°. Work out the area of triangle ABC. Give your answer to 1 decimal place.

9.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.

10.A television cable runs in a straight line from the edge of a flat roof 20 m above the ground to a bracket on a wall 5 m above the ground. The horizontal distance between the roof edge and the bracket is 15 m. Work out the length of the cable. Give your answer to 1 decimal place.

11.A parallelogram has an area of 54 cm² and a base of 9 cm. Work out its perpendicular height.

12.A rhombus-shaped floor tile has sides of length 12 cm and an interior angle of 55°. Work out the area of the tile. Give your answer to 1 decimal place.

13.A tap fills a tank at a rate of 18 litres per minute. The tank holds 0.45 m³. Work out how long the tap takes to fill the tank.

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

15.The area of triangle ABC is 42 cm². AB = 9.5 cm and angle BAC = 61°. Work out the length of AC. Give your answer to 1 decimal place.