Geometry and measures worksheet — GCSE Foundation

1.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.

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

3.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).

4.A hexagonal prism has 8 faces and 12 vertices. Using F + V − E = 2, work out how many edges it has.

5.Triangle ABC has angle A = 40°, angle B = 65° and AB = 10 cm. Triangle DEF has angle D = 40°, angle E = 65° and DE = 10 cm. Which condition proves the two triangles are congruent?

6.A sector of a circle has radius 8 cm and takes up three-quarters of the full circle. Work out the perimeter of the sector, in terms of π.

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 cuboid measures 5 cm long (left to right), 3 cm deep (front to back) and 2 cm tall. Its front elevation is 5 cm wide by 2 cm high. Its side elevation is 3 cm wide by 2 cm high. What are the dimensions of its plan view, looking down from above?

9.Write down the exact value of tan 45°.

10.A circle has two straight radii drawn from the centre to the edge, together with the arc between them. Write down the name of the region enclosed by these two radii and the arc.

11.A shop stacks tins in a display block. The front elevation of the block is 4 tins wide and 3 tins high. The side elevation shows the block is 2 tins deep. Every position in the block is filled. How many tins are used in total?

12.A ramp is built from two straight metal supports that rest on the flat ground and meet each other at the top, forming a triangle with the ground. One support meets the ground at 34°. The angle between the two supports where they meet is 71°. Work out the angle between the second support and the ground.

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

14.In the RHS congruence condition, which three facts must be true about two triangles for RHS to prove they are congruent?

15.A circle has a radius of 1 cm. Work out the circumference of the circle. Give your answer in terms of π.