Geometry and measures worksheet — GCSE Foundation

1.In kite WXYZ, WX = WZ and XY = ZY (so at each of X and Z, one side from each of the two unequal pairs meets). Angle X = 100°. Work out angle Z.

2.Two points on a circle divide its circumference into two arcs of different lengths. Write down the name given to the shorter of the two arcs.

3.A sector of a circle has an angle of 90° at the centre. Write down what fraction of the whole circle this sector represents.

4.A solid metal sphere has a radius of 5 cm. It is melted down and recast into a solid cylinder with the same radius, 5 cm. Work out the height of the cylinder, so that its volume equals the volume of the sphere. Use π = 3.14 and give your answer correct to 1 decimal place.

5.A sector of a circle has radius 15 cm and angle 216°. Using π = 3.14, work out the arc length of the sector.

6.The diagram shows a prism resting on a table. Which shape is its front elevation, the view looking at it from directly in front?

7.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.

8.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.

9.A rhombus has all four sides equal in length. Write down how many pairs of parallel sides a rhombus has.

10.P is the point (3, 4) and Q is the point (6, 0). Work out the distance of each point from the origin, and write down which point is closer to the origin.

11.A rectangular photograph has an area of 96 cm². One of its sides is 8 cm long. Work out the length of the other side.

12.A sector of a circle has radius 4 cm and angle 90°. Using π = 3.14, work out the area of the sector.

13.A rectangular photograph is 12 cm long and 5 cm wide. Work out the perimeter of the photograph.

14.Triangle ABC has angle A = 40°, angle B = 65° and AB = 10 cm. Triangle DEF has angle D = 40°, angle E = 65° and DE = 10 cm. Which condition proves the two triangles are congruent?

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?