Geometry and measures worksheet — GCSE Foundation

1.The diagram shows the plan, front elevation and side elevation of a solid. Which solid could this be?

2.How many vertices does a square-based pyramid have?

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

4.A landscaper marks out two triangular flower beds using stakes and a tape measure. Bed 1 has two edges of 5 m and 7 m, meeting at a corner with a marked angle of 60° between them. Bed 2 has edges of 5 m and 7 m, meeting at a corner also marked at 60° between them. The landscaper wants to check the two beds will be exactly the same size and shape using only these three measurements. Which condition proves the two beds are congruent?

5.The three angles of a triangle are 10°, 58° and 112°. Write down the name that describes this triangle.

6.A trapezium has parallel sides of 16 cm and 24 cm, and a perpendicular height of 7 cm. Work out the area of the trapezium.

7.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?

8.A ladder rests against a wall, making an angle of 60° with the ground. The ladder is 2 m long. Using the exact value of sin 60°, work out how high up the wall the ladder reaches, giving your answer in centimetres.

9.A triangular badge has two sides of length 8 cm and a third side of length 5 cm. Work out the perimeter of the badge.

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

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

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

13.The perimeter of a square is 20 cm. Work out the area of the square.

14.A shop stacks identical storage crates in a display. The diagram shows the plan of the floor positions used, with one corner position marked. Every floor position is filled with crates stacked 3 high, except the marked corner position, which is left completely empty. Work out how many crates are used in total.

15.The cross-section of a tent is an isosceles triangle. The angle at the top, between the two equal sloping sides, is 62°. The other two angles are equal to each other. Work out the size of each of those two angles.