Geometry and measures worksheet — GCSE Foundation

1.A builder lays a low wall made from identical bricks. The diagram shows the plan of the wall's footprint on a grid, where each square is one brick. The wall is built up to a height of 4 bricks everywhere. Work out the total number of bricks used.

2.A circular clock face has a diameter of 18 cm. Work out the circumference of the clock face. Use π = 3.14.

3.A garden designer describes a flower bed as a shape with four straight sides: exactly one pair of sides is parallel, those two parallel sides are different lengths, and the other two sides are equal in length to each other but not parallel to each other. Which shape should the designer draw?

4.Triangle T has a vertex at (2, 1). It is enlarged by a scale factor of 3, centre (0, 0). Work out the coordinates of the image of this vertex.

5.A path goes from A(1, 1) to B(1, 5), then from B to C(6, 5). Work out the total length of the path from A to C.

6.ABCD is an isosceles trapezium. The sides AB and DC are parallel, and the two sloping sides AD and BC are equal in length. Angle D is 112°. Work out the size of angle B.

7.A sector of a circle has an angle of 90° at the centre. Write down what fraction of the whole circle this sector represents.

8.A shop sells a scale model of a van. The model and the real van are similar shapes, with lengths in the ratio 1 : 24. The model is 18.5 cm long. Work out the length of the real van, giving your answer in metres.

9.Two points on a circle divide its circumference into two arcs of different lengths. Write down the name given to the shorter of the two arcs.

10.A scale model of a bridge is built so that 2 cm on the model represents 5 m of the real bridge. The real bridge is 45 m long. Work out the length of the model bridge, in centimetres.

11.A parallelogram has a base of 9 cm and a perpendicular height of 6 cm. Work out the area of the parallelogram.

12.Write down the exact value of sin 45°.

13.Point D is at (3, 7). It is reflected in the line y = x. Work out the coordinates of the image of point D.

14.Write down the exact value of cos 60°.

15.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.