Geometry and measures worksheet — GCSE Higher

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

2.In triangle ABC, AB = 8.6 cm, AC = 11.4 cm and angle BAC = 47°. Work out the area of triangle ABC. Give your answer to 1 decimal place.

3.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?

4.A parallelogram-shaped tile has two sides of 6 cm and 9 cm, with an angle of 60° between them. Work out the area of the tile. Give your answer to 1 decimal place.

5.A shop sells rice in packs of 250 g. Aisha buys 4 packs. Work out the total mass of rice she buys, in kilograms.

6.In triangle OAB, OA = a and OB = b. P lies on AB such that AP is twice PB. Express the vector OP in terms of a and b.

7.Two identical ladders lean against the same vertical wall from opposite sides, each making an angle of 58.2° with the ground. The two ladders and the ground form a triangle. Work out the size of the angle between the two ladders at the top, where they meet.

8.In triangle ABC, AB = 8 cm, AC = 7 cm and the area of the triangle is 24 cm². Given that angle BAC is acute, work out the size of angle BAC. Give your answer to 1 decimal place.

9.A regular pentagon has centre O. Each vertex is 8 cm from O, and each of the 5 triangles formed by joining O to the vertices is isosceles with an angle of 72° at O. Work out the area of the pentagon. Give your answer to 1 decimal place.

10.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.

11.A right-angled triangle has a hypotenuse of 10 cm. One of its other angles is 45°. Work out the exact length of one of the two shorter sides.

12.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?

13.A surveyor is marking out field ABCD for a new crop. The plan states that side AB is parallel to side DC, but AB and DC are not equal in length, and sides BC and AD are not parallel to each other. Which term correctly describes the shape of field ABCD?

14.A map has a scale of 1 : 20 000. The distance between two villages is 3.4 km in real life. How long is this distance on the map, in centimetres?

15.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.