Geometry and measures worksheet — GCSE Foundation

1.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.

2.A vertical flagpole casts a shadow 6 m long at the same time as a 1.2 m vertical post casts a shadow 1.8 m long. The flagpole and the post are both vertical, and the triangles formed by each object, its shadow, and the sun's ray are similar. Work out the height of the flagpole.

3.A sector of a circle has radius 9 cm and angle 60°. Using π = 3.14, work out the area of the sector, to 1 decimal place.

4.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.

5.A sector of a circle has radius 7 cm and angle 90°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.

6.A rectangular tile measures 4.5 cm by 6 cm. Work out the area of the tile.

7.A car's windscreen wiper blade is 40 cm long and sweeps through an angle of 110° as it wipes the glass. Using π = 3.14, work out the area of glass it wipes, to the nearest cm².

8.A round cake has a radius of 10 cm. Icing costs £0.02 per square centimetre. One slice of the cake is a sector with an angle of 90°. Using π = 3.14, work out the cost of icing the top of that slice, to the nearest penny.

9.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.

10.A triangular prism has a cross-section that is a triangle with a base of 3.5 cm and a perpendicular height of 4 cm. The prism is 10 cm long. Work out the volume of the prism.

11.A circular clock face has a radius of 9 cm. Work out the circumference of the clock face. Use π = 3.14. Give your answer to 1 decimal place.

12.A birthday cake is a cylinder of radius 10 cm and height 8 cm, with a thin ribbon fixed exactly once around the curved side, at half the height, and joined with no overlap. Work out the length of ribbon needed. Use π = 3.14.

13.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.

14.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?

15.A right-angled triangle has a hypotenuse of 10 cm. One of its other angles is 45°. Work out the exact length of one of the two shorter sides.