Geometry and measures worksheet — GCSE Foundation

1.A scale drawing of a rectangular lawn uses a scale of 1 : 125. On the drawing, the lawn measures 4 cm by 2.4 cm. Work out the perimeter of the real lawn, in metres.

2.A hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?

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

4.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.

5.A right-angled triangle has a hypotenuse of 10 cm and one of its other angles is 45°. Work out the length of one of the two shorter sides. Give your answer to 1 decimal place.

6.A wooden block is a cuboid measuring 2 cm by 10 cm by 15 cm. Work out the volume of the block.

7.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.

8.A goat is tied by a rope 7 m long to a post at a corner of a rectangular field, where two fences meet at a right angle. The goat can reach anywhere inside the field that the rope allows. Using π = 3.14, work out the area the goat can graze, to the nearest square metre.

9.A circle has circumference 31.4 cm. Using π = 3.14, work out the radius of the circle.

10.A square-based pyramid is cut by a flat plane parallel to its base, partway up between the base and the apex. What shape is the cross-section?

11.A triangular flag has a base of 40 cm and a perpendicular height of 25 cm. Work out its area.

12.A cuboid-shaped shipping crate has a length of 12 m, a width of 5 m, and a volume of 360 m³. Work out the height of the crate, in metres.

13.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.

14.A hiker walks on a bearing of 065°. She then turns clockwise through 90° and continues walking in a straight line. What bearing is she now walking on?

15.A furniture catalogue drawing uses a scale of 1 cm to 1.5 m. A sofa in the drawing is measured as 7 cm long. What is the real length of the sofa, in metres?