Geometry and measures worksheet — GCSE Foundation

1.A window is made from a rectangle with a semicircle on top. The rectangle is 40 cm wide and 60 cm tall. The semicircle has the same width as the rectangle. Work out the total area of the window. Use π = 3.14. Give your answer to the nearest whole number.

2.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.

3.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?

4.A ship's radar can detect other ships up to 20 km away, over a sector-shaped area with angle 90°. A monitoring company charges £0.50 per square kilometre covered by one radar sweep. Using π = 3.14, work out the total charge for one sweep.

5.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?

6.Three angles meet at a single point on one side of a straight line. Two of the angles are 48° and 65°. Work out the third angle.

7.A solid rubber ball has a radius of 3 cm. Work out the volume of the ball. Use π = 3.14.

8.A kitchen scale is marked in equal divisions of 20 g. The pointer rests three divisions past the 400 g mark. Work out the reading on the scale.

9.A hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?

10.A line segment is measured with a ruler and found to be 6.5 cm long. What is this length in millimetres?

11.Two straight roads cross at a junction. The angle between them, measured with a protractor, is 118°. What is the size of the angle vertically opposite to it?

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

13.A fish tank is a cuboid measuring 40 cm long, 25 cm wide and 30 cm high. Water is poured in to a depth of 20 cm. Work out the volume of water in the tank, in litres.

14.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.

15.A birthday cake is a cylinder of radius 10 cm and height 8 cm, with a thin ribbon fixed exactly once around the curved side, at half the height, and joined with no overlap. Work out the length of ribbon needed. Use π = 3.14.