Geometry and measures worksheet — GCSE Higher

1.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?

2.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.

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

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

5.In triangle ABC, AB = 12 cm, AC = 9 cm and angle BAC = 55°. Work out the size of angle ABC. Give your answer to 1 decimal place.

6.A round cake has a radius of 10 cm. Icing costs £0.02 per square centimetre. One slice of the cake is a sector with an angle of 90°. Using π = 3.14, work out the cost of icing the top of that slice, to the nearest penny.

7.A shape is reflected in the x-axis and the image is then reflected in the y-axis. Which single transformation is equivalent to this combination for every point?

8.A triangular sail for a small boat has a base of 2.4 m and a height of 1.75 m. Sailcloth costs £12.50 per m². Work out the total cost of the sailcloth needed for the sail.

9.In triangle ABC, AB = 9 cm, BC = 6 cm and angle BAC = 35°. This description fits two different triangles. Work out the two possible sizes of angle ACB, each to 1 decimal place.

10.Point P has coordinates (2, 1). Transformation A reflects a point in the x-axis. Transformation B translates a point by the vector (0, 4). Work out the coordinates of the image of P when A is applied first, followed by B.

11.A circular pizza base has a radius of 12 cm. Work out the area of the pizza base. Use π = 3.14.

12.In triangle ABC, AB = 13 cm, AC = 9 cm and angle ABC = 35°. Given that angle ACB is obtuse, work out its size. Give your answer to 1 decimal place.

13.A model of a bridge is built to a scale where every length on the model is 1/240 of the matching length on the real bridge. A support beam on the model measures 3.6 cm. Work out the length of the real support beam, giving your answer in metres.

14.In triangle ABC, AB = 9 cm, AC = 6 cm and angle BAC = 110°. Work out the length of BC. Give your answer to 1 decimal place.

15.A ramp is built from two straight metal supports that rest on the flat ground and meet each other at the top, forming a triangle with the ground. One support meets the ground at 34°. The angle between the two supports where they meet is 71°. Work out the angle between the second support and the ground.