Geometry and measures worksheet — GCSE Foundation

1.A sector of a circle has radius 6 cm and an area of 4.71 cm². Using π = 3.14, work out the angle of the sector.

2.Two similar ponds have perimeters in the ratio 4 : 11. The perimeter of the larger pond is 88 m. Work out the perimeter of the smaller pond.

3.A circle has diameter 10 cm. Using π = 3.14, work out the circumference of the circle.

4.In a right-angled triangle one of the other two angles is 45°, and the side opposite that 45° angle is 7 cm. Work out the length of the hypotenuse. Give your answer to 1 decimal place.

5.A cylindrical drum and a cuboid box are being wrapped for a display. A shop assistant wraps only the flat faces of each item, not any curved surface. How many flat faces in total does the assistant wrap across both items?

6.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.

7.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.

8.A cube has all of its edges the same length. How many planes of symmetry does it have?

9.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?

10.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?

11.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.

12.A path goes from A(1, 1) to B(1, 5), then from B to C(6, 5). Work out the total length of the path from A to C.

13.A sector of a circle has radius 9 cm and angle 40°. Work out the area of the sector, in terms of π.

14.A solid pyramid has a square base of side 10 cm and four identical triangular faces. Its apex is directly above the centre of the base, at a vertical height of 12 cm, and the slant height of each triangular face — the distance from the apex to the midpoint of a base edge — is 13 cm. Work out the total surface area of the pyramid.

15.Work out the exact value of sin 45° × cos 45°.