Geometry and measures worksheet — GCSE Foundation

1.A footpath sign shows a distance of 0.45 km to the next village. Work out this distance in metres.

2.Two vertical masts stand on level ground, 40 m apart. One mast is 30 m tall and the other is 50 m tall. Work out the straight-line distance between the tops of the two masts. Give your answer to 1 decimal place.

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

4.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.

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

6.A goat is tied by a rope 7 m long to a post at a corner of a rectangular field, where two fences meet at a right angle. The goat can reach anywhere inside the field that the rope allows. Using π = 3.14, work out the area the goat can graze, to the nearest square metre.

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.Two angles lie on a straight line. One angle is 37°. Work out the size of the other angle.

9.A bead starts at position (2, −1) on a grid, in centimetres. It is moved by the column vector u, with top number 3 and bottom number 5, and then moved by the column vector v, with top number −7 and bottom number 2. Work out the coordinates of the bead's final position.

10.A tap fills a tank at a rate of 18 litres per minute. The tank holds 0.45 m³. Work out how long the tap takes to fill the tank.

11.A parallelogram has an area of 136 cm² and a base of 17 cm. Work out the perpendicular height of the parallelogram.

12.A sector of a circle has radius 7 cm and angle 90°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.

13.A footpath is 3750 m long. Work out this distance in kilometres.

14.A model of a bridge is built to a scale where every length on the model is 1/240 of the matching length on the real bridge. A support beam on the model measures 3.6 cm. Work out the length of the real support beam, giving your answer in metres.

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