Geometry and measures worksheet — GCSE Foundation

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

2.Shape S has an area of 48 cm². It is enlarged by a scale factor of 1/4 to give shape T. Work out the area of shape T.

3.In a construction, a point P is marked at the foot of the perpendicular drawn from point X to a straight line. Which statement correctly compares the distance XP with the distance from X to any other point on the line?

4.A straight line passes through points A, B and C, with B between A and C. A fourth point D is not on the line. Angle ABD = 132°. Work out the size of angle DBC.

5.A cylindrical drum and a cuboid box are being wrapped for a display. A shop assistant wraps only the flat faces of each item, not any curved surface. How many flat faces in total does the assistant wrap across both items?

6.A solid pyramid has a square base of side 10 cm and four identical triangular faces. Its apex is directly above the centre of the base, at a vertical height of 12 cm, and the slant height of each triangular face — the distance from the apex to the midpoint of a base edge — is 13 cm. Work out the total surface area of the pyramid.

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

8.Every point on a circle is exactly the same distance from one particular point. Write down the name of that point.

9.A right-angled triangle has two sides of length 5 cm and 12 cm, and the angle between those two sides is 90°. Work out the length of the hypotenuse.

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

11.A circular plate has a diameter of 20 cm. Work out the area of the plate. Use π = 3.14.

12.The diagram shows a prism resting on a table. Which shape is its front elevation, the view looking at it from directly in front?

13.The diagram shows the plan of the base layer of a solid built from identical cubes. A second layer of cubes is added on top, filling the entire base layer to a height of 2 cubes everywhere. Work out how many squares are visible in the plan view of this solid.

14.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.

15.Write down the exact value of cos 45°.