Geometry and measures worksheet — GCSE Foundation

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

2.A circular decoration has a radius of 10 cm. A ribbon costs £0.50 per centimetre and is fixed along the curved edge (the arc) of a sector-shaped section with an angle of 90°. Using π = 3.14, work out the cost of the ribbon for this section.

3.A vertical line passes through the point (5, 2). Write down the equation of this line.

4.The top of a clock tower is 25 m above level ground. Oliver stands on the ground 25 m from the foot of the tower. Work out the angle of elevation of the top of the tower from the point where Oliver stands.

5.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.

6.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.

7.A parallelogram has an area of 136 cm² and a base of 17 cm. Work out the perpendicular height of the parallelogram.

8.A sector of a circle has radius 6 cm and angle 60°. Work out the arc length of the sector, in terms of π.

9.A fish tank is a cuboid measuring 40 cm long, 25 cm wide and 30 cm high. Water is poured in to a depth of 20 cm. Work out the volume of water in the tank, in litres.

10.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.

11.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.

12.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.

13.A trapezium-shaped garden bed has parallel sides of 2.5 m and 4.5 m, and a perpendicular width of 3 m. A gardener wants to know the area of the bed before ordering topsoil. Work out the area of the garden bed.

14.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.

15.A photocopier enlarges a document so that every length is multiplied by the same scale factor. A line on the original document is 3.2 cm long, and the same line measures 11.2 cm on the enlarged copy. A second line on the original document is 2.5 cm long. Work out the length of the second line on the enlarged copy, giving your answer to 2 decimal places.