Geometry and measures worksheet — GCSE Foundation

1.ABCD is an isosceles trapezium. The sides AB and DC are parallel, and the two sloping sides AD and BC are equal in length. Angle D is 112°. Work out the size of angle B.

2.A ship's radar can detect other ships up to 20 km away, over a sector-shaped area with angle 90°. A monitoring company charges £0.50 per square kilometre covered by one radar sweep. Using π = 3.14, work out the total charge for one sweep.

3.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.

4.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.

5.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

6.A quadrilateral has vertices A(1, 1), B(5, 1), C(6, 4) and D(2, 4). By comparing the y-coordinates of A, B and of D, C, write down whether the sides AB and DC are parallel, and give a reason for your answer.

7.How many vertices does a cuboid have?

8.In triangle ABC the angle at A is 90° and BC = 10 cm. For the angle at B, sin B = 3/5. Work out the length of AC.

9.A rectangular notice board measures 150 cm by 80 cm. Work out its area in m².

10.The diagram shows the plan, front elevation and side elevation of a solid. Which of these solids matches all three views?

11.A scale drawing of a bridge uses a scale of 1 : 25. A support beam on the drawing measures 4.4 cm. What is the real length of the beam, in metres?

12.Two triangles are congruent to each other. What does this tell you about their angles and sides?

13.A regular nonagon has 9 sides. Work out the sum of its interior angles.

14.A circle is drawn on a page. Write down how many radii can be drawn in the circle.

15.Point C is at (5, 2). It is reflected in the x-axis. Work out the coordinates of the image of point C.