Geometry and measures worksheet — GCSE Higher

1.A regular octagonal tabletop has centre O. Each vertex is 30 cm from O. Work out the area of the tabletop. Give your answer to the nearest square centimetre.

2.In triangle ABC, AB = 11 cm, AC = 9 cm and the area of the triangle is 45 cm². Given that angle BAC is obtuse, work out the size of angle BAC. Give your answer to 1 decimal place.

3.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?

4.A stage designer is building a triangular platform ABC for a school play. AB = 11.5 m, AC = 8.2 m and angle BAC = 72°, the angle between them. The flooring for the platform costs £15.80 per square metre. Work out the total cost of the flooring, to the nearest pound.

5.A flagpole is 12 m tall. Freya stands 9 m from the base of the flagpole on level ground. Work out the angle of elevation of the top of the flagpole from where Freya stands. Give your answer correct to 1 decimal place.

6.A scale drawing uses a scale of 1 : 60. A path on the drawing is measured as 9.8 cm long. What is the real length of the path, in metres, to 1 decimal place?

7.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.

8.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.

9.A trapezium has an area of 45 cm², a perpendicular height of 5 cm, and one parallel side of length 10 cm. Work out the length of the other parallel side.

10.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.

11.A circle has centre O and radius 10 cm. Points A and B lie on the circle such that angle AOB = 130°. Work out the area of the minor segment cut off by the chord AB. Give your answer to 1 decimal place.

12.Two similar ponds have perimeters in the ratio 4 : 11. The perimeter of the larger pond is 88 m. Work out the perimeter of the smaller pond.

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

14.A solid rubber ball has a radius of 3 cm. Work out the volume of the ball. Use π = 3.14.

15.In triangle ABC, AB = 15 cm, angle BAC = 38° and the area of the triangle is 61 cm². Work out the length of BC. Give your answer to 1 decimal place.