Geometry and measures worksheet — GCSE Foundation

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

2.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.

3.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.

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 trapezium has parallel sides of length 6 cm and 10 cm, and a perpendicular height of 4 cm. Work out its area.

6.A ladder of length 7 m leans against a vertical wall. The foot of the ladder is 3 m from the base of the wall. Work out how high up the wall the ladder reaches. Give your answer correct to 1 decimal place.

7.A sector of a circle has radius 4 cm and angle 90°. Using π = 3.14, work out the area of the sector.

8.A sector of a circle has radius 9 cm and angle 40°. Work out the area of the sector, in terms of π.

9.A television cable runs in a straight line from the edge of a flat roof 20 m above the ground to a bracket on a wall 5 m above the ground. The horizontal distance between the roof edge and the bracket is 15 m. Work out the length of the cable. Give your answer to 1 decimal place.

10.Write down the term for the distance all the way around the edge of a circle.

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.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.

13.A sector of a circle has an angle of 90° and an area of 78.5 cm². Using π = 3.14, work out the radius of the circle.

14.A square has sides of length 7 cm. Work out its area.

15.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.