Geometry and measures worksheet — GCSE Foundation

1.In a right-angled triangle, the side opposite angle θ is 6 cm and the hypotenuse is 10 cm. Work out the size of angle θ. Give your answer correct to 1 decimal place.

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

3.A rectangular notice board measures 150 cm by 80 cm. Work out its area in m².

4.A sector of a circle is bounded by two straight edges and one curved edge. Write down the mathematical term for each of the two straight edges.

5.A trapezium has parallel sides of 5.6 cm and 8.4 cm, and a perpendicular height of 4 cm. Work out the area of the trapezium.

6.Two angles are complementary. One of them is 35°. Work out the size of the other angle.

7.A line segment is measured with a ruler and found to be 6.5 cm long. What is this length in millimetres?

8.Triangle ABC has AB = (2x + 3) cm, BC = 11 cm and angle B = 90°. Triangle DEF has DE = 13 cm, EF = 11 cm and angle E = 90°. Given that the two triangles are congruent by SAS, work out the value of x.

9.Triangle ABC has AB = 5 cm, BC = 7 cm and CA = 9 cm. Triangle DEF has DE = 5 cm, EF = 7 cm and FD = 9 cm. Which condition proves the two triangles are congruent?

10.Triangle XYZ has angle X = 90°. Angle Y = 34°. Work out angle Z.

11.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.

12.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?

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

14.A solid is built from five centimetre cubes, standing side by side on a table in a single straight row. Looking down from directly above (the plan view), how many squares are visible?

15.In triangle ABC and triangle DEF, the angle at A and the angle at D are both 40°, and the angle at B and the angle at E are both 70°. No side lengths are given. Write down whether the two triangles must be similar, with the reason.