Geometry and measures worksheet — GCSE Foundation

1.A sector has an angle of 45°. Priti says: 'The area of the sector is one eighth of the area of the full circle, whatever the radius is.' Is Priti correct?

2.A footpath is 3750 m long. Work out this distance in kilometres.

3.An angle is measured with a protractor as 47°. What type of angle is this?

4.Two triangles are similar. The sides of the first triangle are 3 cm, 4 cm and 5 cm. The shortest side of the second triangle is 9 cm. Work out the scale factor from the first triangle to the second.

5.A triangle has vertices A(0, 0), B(10, 0) and C(5, 12). Work out the area of the triangle.

6.An angle measures 108°. Write down the name given to an angle of this size.

7.A solid is built from centimetre cubes standing on a table. Seen from the front, the left-hand column is 2 cubes high, the middle column is 2 cubes high and the right-hand column is 1 cube high. Work out how many squares make up the front elevation.

8.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.

9.Triangle ABC is drawn. The interior angle bisectors from vertices A and B are constructed and meet at point I inside the triangle. Which statement about point I must be true?

10.A shopkeeper builds a display from two cuboid boxes, shown in the diagram. She wants to cover the front of the display with coloured paper. Work out the total area of the front elevation, in square centimetres.

11.Work out the exact value of (cos 45°)² + (sin 45°)².

12.Every diameter of a circle is an example of a more general type of straight line joining two points on the circle. Which term names that more general type of line?

13.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.

14.A sector of a circle has an angle of 90° and an area of 78.5 cm². Using π = 3.14, work out the radius of the circle.

15.Two straight roads cross at a junction. The angle between them, measured with a protractor, is 118°. What is the size of the angle vertically opposite to it?