Geometry and measures worksheet — GCSE Foundation

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

2.A sector of a circle has radius 9 cm and angle 120°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.

3.A circular pizza base has a radius of 12 cm. Work out the area of the pizza base. Use π = 3.14.

4.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.

5.A garden bed is designed as a trapezium. The two parallel sides are 8 m and 12 m, and the perpendicular distance between them is 5 m. Grass seed covers 4 m² per bag, sold only in whole bags. Work out how many bags of grass seed are needed.

6.A ship sails 12 km on a bearing of 070° from a harbour to a buoy. It then sails a further 9 km, still on a bearing of 070°, from the buoy to a lighthouse. How far is the lighthouse from the harbour, in kilometres?

7.A goat is tied by a rope 7 m long to a post at a corner of a rectangular field, where two fences meet at a right angle. The goat can reach anywhere inside the field that the rope allows. Using π = 3.14, work out the area the goat can graze, to the nearest square metre.

8.Three angles meet at a single point on one side of a straight line. Two of the angles are 48° and 65°. Work out the third angle.

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

10.A hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?

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

12.A sector of a circle has angle 120° and an arc length of 31.4 cm. Using π = 3.14, work out the radius of the circle.

13.A photocopier enlarges a document so that every length is multiplied by the same scale factor. A line on the original document is 3.2 cm long, and the same line measures 11.2 cm on the enlarged copy. A second line on the original document is 2.5 cm long. Work out the length of the second line on the enlarged copy, giving your answer to 2 decimal places.

14.A carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?

15.A church tower is due east of a village. What is the three-figure bearing of the church tower from the village?