Geometry and measures worksheet — GCSE Foundation

1.A sector of a circle has radius 10 cm and angle 150°. Using π = 3.14, work out the perimeter of the sector, to 1 decimal place.

2.A parallelogram has an area of 96 cm² and a base of 8 cm. Work out the perpendicular height of the parallelogram.

3.A circle has circumference 31.4 cm. Using π = 3.14, work out the radius of the circle.

4.A sector of a circle has radius 15 cm and angle 216°. Using π = 3.14, work out the arc length of the sector.

5.Two metal window frames are checked before installation. Frame A has edges of 40 cm and 65 cm, with a marked angle of 35° at the far end of the 65 cm edge, away from where the two given edges meet. Frame B has matching edges of 40 cm and 65 cm, with a matching 35° angle in the same position. The fitter wants to know if these measurements alone guarantee the two frames are congruent. What should the fitter be told?

6.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.

7.Two angles are complementary. One of them is 35°. Work out the size of the other angle.

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

9.In pentagon PQRST, which of the following correctly names the interior angle at vertex R, using standard three-letter angle notation?

10.A triangular bunting flag has two equal sides. The angle between those two equal sides is 80°, and the other two angles of the flag are equal to each other. Work out the size of each of the two equal angles.

11.A trundle wheel has a diameter of 0.5 m. It is rolled along the ground and makes 20 complete turns. Using π = 3.14, work out the total distance rolled, in metres.

12.A line segment joins two points on the circumference of a circle, without necessarily passing through the centre. Write down the general term for this line segment.

13.Work out the exact value of sin 30° + cos 60°.

14.A raised garden bed is a prism whose cross-section is a triangle with a base of 1.2 m and a perpendicular height of 0.8 m. The bed is 3 m long. Work out the volume of soil needed to fill it, in m³.

15.Write down the number of lines of symmetry a rhombus has.