Geometry and measures worksheet — GCSE Foundation

1.A shopkeeper builds a display from two cuboid boxes, shown in the diagram. She wants to cover the front of the display with coloured paper. Work out the total area of the front elevation, in square centimetres.

2.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.

3.A parallelogram has an area of 54 cm² and a base of 9 cm. Work out its perpendicular height.

4.A garden water trough is a prism whose cross-section is a right-angled triangle with base 40 cm and height 30 cm. The trough is 120 cm long. Work out the volume of water needed to fill the trough completely.

5.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?

6.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.

7.A trapezium-shaped garden bed has parallel sides of 2.5 m and 4.5 m, and a perpendicular width of 3 m. A gardener wants to know the area of the bed before ordering topsoil. Work out the area of the garden bed.

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 sector of a circle has radius 6 cm and angle 60°. Work out the arc length of the sector, in terms of π.

10.A cake recipe takes 135 minutes from start to finish. Write this time as hours and minutes.

11.A support strut for a shed roof is in the shape of a right-angled triangle. The two shorter sides of the strut are 5 m and 9 m. Work out the length of the sloping strut (the hypotenuse). Give your answer correct to 1 decimal place.

12.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.

13.A cylinder has a radius of 5 cm. Its volume is 471 cm³. Using π = 3.14, work out the height of the cylinder.

14.A student draws a net using 5 identical squares arranged in a row of four with one extra square attached to the side of one of them. Can this net be folded to make a closed cube?

15.Triangle JKL and triangle MNP are similar, with JK ÷ MN = JL ÷ MP = 2. A student says triangle JKL must be congruent to triangle MNP. Write down why the student is wrong.