Geometry and measures worksheet — GCSE Foundation

1.Sam says: '3.2 litres is the same as 320 ml, because you multiply by 100.' Which statement about Sam's claim is correct?

2.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.

3.A shopkeeper builds a display from two cuboid boxes, shown in the diagram. She wants to cover the front of the display with coloured paper. Work out the total area of the front elevation, in square centimetres.

4.A sector of a circle has radius 9 cm and angle 40°. Work out the area of the sector, in terms of π.

5.In triangle ABC the angle at C is 90°, AC = 8 cm and the angle at A is 30°. Work out the length of BC. Give your answer to 1 decimal place.

6.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?

7.A gardener wants to buy edging trim to go all the way around a circular flower bed with a diameter of 8 m. Work out the length of edging trim needed, using π = 3.14. Give your answer to the nearest metre.

8.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?

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

10.Write down which quadrant contains the point (−3, 5) when plotted on a coordinate grid.

11.Triangle JKL has a right angle at K, hypotenuse JL = 13 cm, and side JK = 5 cm. Triangle MNO has a right angle at N, hypotenuse MO = 13 cm, and side MN = 5 cm. Using only the facts given, and without working out any further lengths, write down the congruence condition that proves triangle JKL is congruent to triangle MNO.

12.Write down the term for the distance all the way around the edge of a circle.

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

14.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?

15.A circular pizza base has a radius of 12 cm. Work out the area of the pizza base. Use π = 3.14.