Geometry and measures worksheet — GCSE Foundation

1.A triangle has a base of 8 cm and a perpendicular height of 5 cm. Work out its area.

2.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.

3.A sector of a circle has radius 6 cm and angle 150°. Using π = 3.14, work out the perimeter of the sector.

4.Triangle PQR and triangle XYZ have angle P = angle X, angle Q = angle Y and angle R = angle Z, with no side lengths given for either triangle. Which of the following correctly describes the relationship between the two triangles?

5.A chord divides a circle into two regions, one larger than the other. Write down the term used for the smaller of these two regions.

6.In triangle ABC the base BC is 10 cm long and the sloping side AB is 13 cm long. The perpendicular height from A down to BC is 12 cm. Work out the area of triangle ABC.

7.A zip wire is fixed at an angle of 50° to the horizontal, running from a high platform down to the ground. The zip wire itself, from the platform to the ground, is 12 m long. Work out the horizontal distance covered by the zip wire. Give your answer correct to 1 decimal place.

8.In triangle ABC, point D lies on side AB and point E lies on side AC, so that DE is parallel to BC. AD = 3 cm, DB = 6 cm and DE = 4 cm. Work out the length of BC.

9.A sprinkler waters a sector-shaped patch of a garden with radius 8 m and angle 90°. Work out the perimeter of the watered sector, to 1 decimal place. (Use π = 3.14.)

10.A chord divides a circle into two segments of different sizes. Write down the name given to the smaller of the two segments.

11.A cone is cut by a flat plane parallel to its circular base, partway up between the base and the apex. What shape is the cross-section?

12.A rhombus has all four sides equal in length. Which statement about a rhombus is correct?

13.Write down the column vector that describes a translation of 5 units to the left and 3 units down.

14.A solid cylinder is lying on its curved side on a table, with its circular ends facing left and right. What shape is its plan view, looking down from above?

15.A circle has a radius of 1 cm. Work out the circumference of the circle. Give your answer in terms of π.