Geometry and measures worksheet — GCSE Foundation

1.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?

2.A submarine travels due south. What is the three-figure bearing for this direction?

3.A sector of a circle has radius 7 cm and angle 90°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.

4.A furniture catalogue drawing uses a scale of 1 cm to 1.5 m. A sofa in the drawing is measured as 7 cm long. What is the real length of the sofa, in metres?

5.A garden water trough is a prism whose cross-section is a right-angled triangle with base 40 cm and height 30 cm. The trough is 120 cm long. Work out the volume of water needed to fill the trough completely.

6.A garden flower bed is in the shape of a trapezium. Its two parallel edges are 3.5 m and 6.5 m long, and the perpendicular distance between them is 4 m. Bedding plants cost £2.50 per square metre to cover the bed. Work out the total cost of the bedding plants.

7.Two similar ponds have perimeters in the ratio 4 : 11. The perimeter of the larger pond is 88 m. Work out the perimeter of the smaller pond.

8.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.

9.A cyclist rides around a perfectly circular track with centre O. At every moment of the ride, the distance from O to the cyclist is exactly the same. Which term names this fixed distance?

10.A triangular flag has a base of 40 cm and a perpendicular height of 25 cm. Work out its area.

11.A surveyor is marking out field ABCD for a new crop. The plan states that side AB is parallel to side DC, but AB and DC are not equal in length, and sides BC and AD are not parallel to each other. Which term correctly describes the shape of field ABCD?

12.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.

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

14.An ice cream is made from a cone of radius 3 cm and height 10 cm, topped with a hemisphere of the same radius sitting exactly on top of the cone. Work out the total volume of the ice cream. Use π = 3.14. Give your answer to the nearest whole number. Volume of a cone = 1/3 × πr²h. Volume of a sphere = 4/3 × πr³.

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