Geometry and measures worksheet — GCSE Foundation

1.A rectangle has vertices A(0, 0), B(6, 0), C(6, 4) and D(0, 4). Work out the length of the diagonal AC. Give your answer correct to 2 decimal places.

2.In triangle ABC the angle at C is 90°, AC = 8 cm and the angle at A is 30°. Work out the length of BC. Give your answer to 1 decimal place.

3.Write down which quadrant contains the point (−3, 5) when plotted on a coordinate grid.

4.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?

5.A parallelogram has an area of 84 cm² and a base of 12 cm. Work out the perpendicular height of the parallelogram.

6.Two straight paths cross at a junction in a park. One of the angles between them, measured with a protractor, is 76°. What is the size of the angle immediately next to it on a straight line?

7.A sector of a circle has radius 12 cm and angle 45°. Using π = 3.14, work out the area of the sector.

8.A trapezium has parallel sides of length 6 cm and 10 cm, and a perpendicular height of 4 cm. Work out its area.

9.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.

10.A sector of a circle has radius 10 cm and angle 72°. Using π = 3.14, work out the arc length of the sector.

11.A circular tabletop has a radius of 15 cm. Work out the area of the tabletop. Use π = 3.14. Give your answer to 1 decimal place.

12.A line segment is measured with a ruler and found to be 6.5 cm long. What is this length in millimetres?

13.A vertical line passes through the point (5, 2). Write down the equation of this line.

14.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?

15.A party hat is in the shape of a cone with a base radius of 6 cm and a slant height of 10 cm. Work out the curved surface area of the party hat. Use π = 3.14 and the formula curved surface area = πrl.