Geometry and measures worksheet — GCSE Foundation

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

2.Write down the exact value of sin 0°.

3.Write down how many right angles a right-angled triangle has.

4.How many edges does a triangular prism have?

5.How many vertices does a cylinder have?

6.A shop sells a scale model of a van. The model and the real van are similar shapes, with lengths in the ratio 1 : 24. The model is 18.5 cm long. Work out the length of the real van, giving your answer in metres.

7.Triangle T has a vertex at (2, 1). It is enlarged by a scale factor of 3, centre (0, 0). Work out the coordinates of the image of this vertex.

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

9.Write down the column vector that describes a translation of 4 units to the right and 4 units up.

10.Two similar shapes have lengths in the ratio 1 : 3. A side of the smaller shape is 4 cm long. Work out the length of the corresponding side of the larger shape.

11.Two identical ladders lean against the same vertical wall from opposite sides, each making an angle of 58.2° with the ground. The two ladders and the ground form a triangle. Work out the size of the angle between the two ladders at the top, where they meet.

12.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?

13.A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 20 cm. Work out the length of the other shorter side.

14.The diagram shows a cuboid. Work out the area of its front elevation, in square centimetres.

15.A stained-glass window panel is designed as a kite. Two adjacent sides are each 25 cm, and the other two adjacent sides are each 40 cm. A frame is fitted around the whole panel. The frame costs £2.50 per metre, sold only in whole metres. Work out the total cost of the frame.