Geometry and measures worksheet — GCSE Higher

1.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.

2.In triangle ABC, AB = 9 cm, angle BAC = 50° and the area of the triangle is 36 cm². Work out the length of AC. Give your answer to 1 decimal place.

3.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?

4.A triangular plot of land ABC is to be covered with turf. AB = 23.5 m, AC = 17.2 m and angle BAC = 108°. Turf costs £4.25 per square metre. Work out the cost of the turf for the plot. Give your answer to the nearest pound.

5.In triangle ABC, angle BAC = 42°, angle ABC = 63° and BC = 8.4 cm. Work out the length of AC. Give your answer to 1 decimal place.

6.In triangle ABC, AB = 12 cm, AC = 7 cm and the area of the triangle is 33 cm². Given that angle BAC is obtuse, work out the size of angle BAC. Give your answer to 1 decimal place.

7.Sam says: '3.2 litres is the same as 320 ml, because you multiply by 100.' Which statement about Sam's claim is correct?

8.Two similar triangles have lengths in the ratio 5 : 8. A side of the smaller triangle is 6.5 cm. Work out the length of the corresponding side of the larger triangle.

9.Points P and Q have coordinates P(0, 0, 0) and Q(5, 7, 9) in a three-dimensional coordinate system, with all lengths in centimetres. Work out the distance PQ. Give your answer correct to 1 decimal place.

10.A vertical line passes through the point (5, 2). Write down the equation of this line.

11.A triangle has one unknown side or angle, marked x. In which one of these situations should the sine rule, rather than the cosine rule, be used to find x?

12.The bearing of a campsite B from a walker's position A is 070°. What is the bearing of A from B?

13.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.

14.A sector of a circle has radius 9 cm and angle 120°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.

15.A carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?