Geometry and measures worksheet — GCSE Foundation

1.The diagram shows a solid built from identical cubes. How many squares are in its plan view, the view looking straight down from above?

2.A solid metal sphere has a radius of 5 cm. It is melted down and recast into a solid cylinder with the same radius, 5 cm. Work out the height of the cylinder, so that its volume equals the volume of the sphere. Use π = 3.14 and give your answer correct to 1 decimal place.

3.A parallelogram has a base of 4 cm and a perpendicular height of 17 cm. Work out the area of the parallelogram.

4.Lines AB and CD cross at a point, forming four right angles where they meet. Which notation correctly describes the relationship between AB and CD?

5.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.

6.A scale drawing of a park uses a scale of 1 : 2000. A path is drawn 8.5 cm long on the drawing. A cyclist rides the length of the path and then rides straight back again along the same path. How far does the cyclist travel in total, in metres?

7.In a right-angled triangle one of the other two angles is 45°, and the side opposite that 45° angle is 7 cm. Work out the length of the hypotenuse. Give your answer to 1 decimal place.

8.Point C is at (5, 2). It is reflected in the x-axis. Work out the coordinates of the image of point C.

9.A trapezium has an area of 45 cm², a perpendicular height of 5 cm, and one parallel side of length 10 cm. Work out the length of the other parallel side.

10.A solid has 6 faces and 8 vertices. Using the formula F + V − E = 2, work out how many edges it has.

11.A garden plan is drawn to a scale of 1 cm : 1.8 m. A path on the plan measures 4.5 cm. What is the real length of the path, in metres, to 1 decimal place?

12.A square-based pyramid has a square base and four identical triangular sloping faces, with its apex directly above the centre of the base. How many planes of symmetry does it have?

13.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.

14.A conservatory has a roof panel shaped like a regular octagon. Work out the interior angle of the octagon, then use it to work out the size of the reflex angle at the same vertex, on the outside of the roof panel.

15.Write down the exact value of sin 0°.