Geometry and measures worksheet — GCSE Foundation

1.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.

2.In triangle ABC and triangle DEF, AB = DE, angle ABC = angle DEF and BC = EF. Write down the congruence condition that proves the two triangles are congruent.

3.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.

4.A sector of a circle has radius 10 cm and angle 150°. Using π = 3.14, work out the perimeter of the sector, to 1 decimal place.

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

6.A ship's radar can detect other ships up to 20 km away, over a sector-shaped area with angle 90°. A monitoring company charges £0.50 per square kilometre covered by one radar sweep. Using π = 3.14, work out the total charge for one sweep.

7.A carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?

8.A right-angled triangle has a hypotenuse of 8 cm, and one of its shorter sides is 4 cm. Work out the size of the angle between that 4 cm side and the hypotenuse.

9.A solid cone has a base radius of 6 cm and a vertical height of 10 cm. Work out the volume of the cone. Use π = 3.14 and give your answer correct to 1 decimal place.

10.A kitchen scale is marked in equal divisions of 20 g. The pointer rests three divisions past the 400 g mark. Work out the reading on the scale.

11.A sector of a circle has angle 120° and an arc length of 31.4 cm. Using π = 3.14, work out the radius of the circle.

12.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

13.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.

15.A shop sells rice in packs of 250 g. Aisha buys 4 packs. Work out the total mass of rice she buys, in kilograms.