Geometry and measures worksheet — GCSE Foundation

1.A quadrilateral has angles of 100°, 85° and 95° at three of its vertices. Work out the fourth angle.

2.A sector of a circle has radius 9 cm and angle 40°. Work out the area of the sector, in terms of π.

3.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.

4.Write down the term for the distance all the way around the edge of a circle.

5.A circular garden pond has a diameter of 5 m. A gardener is laying gravel around it in a ring-shaped path 1 m wide, measured outward from the edge of the pond. Work out the area of the gravel path. Use π = 3.14.

6.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?

7.A sector of a circle has radius 6 cm and angle 60°. Work out the arc length of the sector, in terms of π.

8.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.

9.A sector of a circle has radius 4 cm and angle 90°. Using π = 3.14, work out the area of the sector.

10.In a right-angled triangle, the two shorter sides are a and b, and the hypotenuse is c. Write down the correct statement of Pythagoras' theorem.

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

12.A cylinder has a radius of 5 cm. Its volume is 471 cm³. Using π = 3.14, work out the height of the cylinder.

13.A parallelogram has an area of 54 cm² and a base of 9 cm. Work out its perpendicular height.

14.A circle has two straight radii drawn from the centre to the edge, together with the arc between them. Write down the name of the region enclosed by these two radii and the arc.

15.A bus journey takes 2.5 hours. Work out how many minutes this is.