Geometry and measures worksheet — GCSE Higher

1.A hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?

2.A model car is built to a scale of 1 : 24. The real car is 4.32 m long. Work out the length of the model, in centimetres.

3.A garden is made of two triangular flower beds, ABC and ACD, joined along the edge AC. In triangle ABC, angle ABC = 90°, AB = 5 m and BC = 12 m. In triangle ACD, AD = 9 m and angle CAD = 40°, the angle between AC and AD. Work out the area of flower bed ACD. Give your answer to 1 decimal place.

4.Two bronze statues are geometrically similar and made from the same solid bronze. Their heights are 30 cm and 45 cm. The smaller statue has a mass of 12 kg. Work out the mass of the larger statue, in kg.

5.A circular tabletop has a radius of 15 cm. Work out the area of the tabletop. Use π = 3.14. Give your answer to 1 decimal place.

6.Two coastguard stations A and B are 18 km apart, with B due east of A. A boat at C is on a bearing of 062° from A and on a bearing of 315° from B. Work out the distance of the boat from station B. Give your answer to 1 decimal place.

7.A solid ball has a radius of 7 cm. Work out the surface area of the ball. Use π = 3.14.

8.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?

9.A field ABCD is a convex quadrilateral. AB = 40 m, BC = 32 m and angle ABC = 95°. The other two sides are CD = 25 m and DA = 36 m. Work out the area of the field. Give your answer to the nearest square metre.

10.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.

11.In a right-angled triangle, the side opposite angle θ is 6 cm and the hypotenuse is 10 cm. Work out the size of angle θ. Give your answer correct to 1 decimal place.

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

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

14.In triangle ABC the angle at C is 90°, AC = 8 cm and the angle at A is 30°. Work out the length of BC. Give your answer to 1 decimal place.

15.A circle has two straight radii drawn from the centre to the edge, together with the arc between them. Write down the name of the region enclosed by these two radii and the arc.