Geometry and measures worksheet — GCSE Higher

1.A circular garden pond has a diameter of 5 m. A gardener is laying gravel around it in a ring-shaped path 1 m wide, measured outward from the edge of the pond. Work out the area of the gravel path. Use π = 3.14.

2.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?

3.PT is a tangent to a circle with centre O, touching the circle at T. OT is a radius. Angle OPT = 27°, where P is a point outside the circle. Work out the size of angle POT.

4.A textbook contains the instruction 'Draw AB' and, on the next line, the statement 'AB = 5 cm'. Which statement about the notation AB is correct?

5.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.

6.A ship sails 12 km on a bearing of 070° from a harbour to a buoy. It then sails a further 9 km, still on a bearing of 070°, from the buoy to a lighthouse. How far is the lighthouse from the harbour, in kilometres?

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

8.A cylinder has a radius of 5 cm. Its volume is 471 cm³. Using π = 3.14, work out the height of the cylinder.

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

10.Two traffic cones are geometrically similar. The smaller cone has height 6 m and the larger cone has height 9 m. Work out the ratio of the volume of the smaller cone to the volume of the larger cone, giving your answer in the form a : b in its simplest form.

11.A triangular plot of land has sides AB = 13 m and AC = 10 m, with angle BAC = 72° between them. Work out the perimeter of the plot. Give your answer to 1 decimal place.

12.Shape S is enlarged by a scale factor of −3 about a fixed centre. Which statement correctly describes the image compared to the original shape?

13.A triangular prism has a cross-section that is a triangle with a base of 3.5 cm and a perpendicular height of 4 cm. The prism is 10 cm long. Work out the volume of the prism.

14.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?

15.In triangle ABC, AB = 15.6 cm, AC = 8.9 cm and angle BAC = 112°, the angle between them. Work out the area of triangle ABC. Give your answer to 1 decimal place.