Geometry and measures worksheet — GCSE Foundation

1.A cuboid has a length, width and height that are all different from each other. How many planes of symmetry does it have?

2.A(1, 2), B(5, 2) and C(5, 6) are three of the four vertices of a square ABCD. Work out the coordinates of D.

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

4.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?

5.The point (0, −5) lies on one of the two coordinate axes. Write down which axis this is.

6.Two sides of a triangle are 20 cm and 8 cm long. Write down which one of these lengths is possible for the third side.

7.A solid cone has a base radius of 6 cm and a vertical height of 10 cm. Work out the volume of the cone. Use π = 3.14 and give your answer correct to 1 decimal place.

8.Two similar hexagonal tiles have lengths in the ratio 4 : 7. A side of the smaller tile is 8.4 cm long. Work out the length of the corresponding side of the larger tile.

9.A polygon has 9 sides. What is the name of this polygon?

10.A photograph is 10 cm wide and 15 cm tall. It is enlarged to make a similar poster that is 40 cm wide. The poster costs £0.80 per centimetre of its height to print, based on its full height. Work out the cost of printing the poster.

11.A wooden block is a cuboid measuring 2 cm by 10 cm by 15 cm. Work out the volume of the block.

12.A ship's radar shows a lighthouse at the point (12, −4) on a grid measured in nautical miles. The ship is at (2, 5). The ship sails along the vector that takes it directly to the lighthouse, then sails along that same vector again. Work out the ship's final position.

13.Write down the exact value of tan 0°.

14.A straight line passes through points A, B and C, with B between A and C. A fourth point D is not on the line. Angle ABD = 132°. Work out the size of angle DBC.