Geometry and measures worksheet — GCSE Higher

1.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.

2.In triangle ABC, BC = 8 cm, AC = 10 cm and angle BAC = 40°. Given that angle ABC is acute, work out its size. Give your answer to 1 decimal place.

3.In triangle ABC, angle ABC = 72° and angle ACB = 48°. Side AB = (2x + 1) cm and side AC = (3x − 2) cm. Work out the value of x. Give your answer to 1 decimal place.

4.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.

5.A circular pizza base has a radius of 12 cm. Work out the area of the pizza base. Use π = 3.14.

6.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?

7.A fan-shaped rug is in the shape of a sector of a circle with radius 4 m and angle 180°. It costs £4 per square metre to make. Using π = 3.14, work out the total cost of the rug.

8.A zip wire is fixed at an angle of 50° to the horizontal, running from a high platform down to the ground. The zip wire itself, from the platform to the ground, is 12 m long. Work out the horizontal distance covered by the zip wire. Give your answer correct to 1 decimal place.

9.A sector of a circle has radius 12 cm and angle 45°. Using π = 3.14, work out the area of the sector.

10.In triangle ABC, AB = 8 cm, BC = 11 cm and AC = 6 cm. Work out the size of angle ABC. Give your answer to 1 decimal place.

11.A photograph is 10 cm wide and 15 cm tall. It is enlarged to make a similar poster that is 40 cm wide. The poster costs £0.80 per centimetre of its height to print, based on its full height. Work out the cost of printing the poster.

12.A solid metal sphere has a radius of 5 cm. It is melted down and recast into a solid cylinder with the same radius, 5 cm. Work out the height of the cylinder, so that its volume equals the volume of the sphere. Use π = 3.14 and give your answer correct to 1 decimal place.

13.A plumber charges a £45 call-out fee, plus £28 for each hour worked. She works on a job for 3 hours 30 minutes, and her hours are billed by rounding up to the next whole hour. Work out the total amount she charges.

14.A sector of a circle has radius 6 cm and an area of 4.71 cm². Using π = 3.14, work out the angle of the sector.

15.A cuboid has a rectangular base measuring 6 cm by 8 cm, and a height of 4 cm. Work out the angle between the diagonal from a base corner to the opposite top corner, and the base of the cuboid. Give your answer correct to 1 decimal place.