Geometry and measures worksheet — GCSE Foundation

1.Which of the following correctly describes what it means for two lines to be perpendicular?

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

3.A parallelogram has a base of 20 cm and a sloping side of 13 cm. The perpendicular drawn from the top of that sloping side down to the base meets the base 5 cm from the foot of the sloping side, so the perpendicular, the 5 cm and the 13 cm sloping side form a right-angled triangle. Work out the area of the parallelogram.

4.Triangle T has a vertex at (8, 4). It is enlarged by a scale factor of 1/2, centre (2, 4). Work out the coordinates of the image of this vertex.

5.Triangle PQR has vertices P(0, 0), Q(6, 0) and R(0, 8). Work out the perimeter of the triangle.

6.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?

7.Point C is at (2, 3). It is rotated 90° clockwise about the origin. Work out the coordinates of the image of point C.

8.Which pair of points lies on a horizontal line when the points are plotted on a coordinate grid?

9.A parallelogram has a base of 9 cm and a perpendicular height of 4 cm. Work out its area.

10.A rectangular photograph has an area of 96 cm². One of its sides is 8 cm long. Work out the length of the other side.

11.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?

12.A sector of a circle is bounded by two straight edges and one curved edge. Write down the mathematical term for each of the two straight edges.

13.A cylinder has a radius of 3 cm and a height of 10 cm. Using π = 3.14, work out the volume of the cylinder.

14.A circular clock face has a radius of 9 cm. Work out the circumference of the clock face. Use π = 3.14. Give your answer to 1 decimal place.

15.The diagram shows the plan view and the front elevation of a cuboid-shaped box, each drawn as a rectangle. Work out the area of the box's side elevation, in square centimetres.