Geometry and measures worksheet — GCSE Foundation

1.Write down the mathematical name for a quadrilateral that has exactly one pair of parallel sides.

2.A vertical flagpole casts a shadow 6 m long at the same time as a 1.2 m vertical post casts a shadow 1.8 m long. The flagpole and the post are both vertical, and the triangles formed by each object, its shadow, and the sun's ray are similar. Work out the height of the flagpole.

3.A solid cube has a volume of 8 cm³. Work out the length of one edge of the cube.

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

5.The diagram shows a solid made from two cuboids joined together. Which shape is the front elevation of this solid?

6.Lines PQ and RS are parallel. A straight line crosses PQ at point X and crosses RS at point Y. Angle PXY = 63°. Angle PXY and angle XYS are co-interior (allied) angles, which add up to 180°. Work out the size of angle XYS.

7.How many vertices does a cylinder have?

8.Write down the column vector, from the options given, that would move a point to the right and downwards.

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 solid pyramid has a square base of side 10 cm and four identical triangular faces. Its apex is directly above the centre of the base, at a vertical height of 12 cm, and the slant height of each triangular face — the distance from the apex to the midpoint of a base edge — is 13 cm. Work out the total surface area of the pyramid.

11.At a point on a straight line, two angles are formed. One of them is 63°. Work out the size of the other angle.

12.Priya says: 'To find the arc length of a sector, you divide the circumference by the angle in degrees.' Which statement about Priya's method is correct?

13.Triangle DEF has a right angle at E. Angle DFE = 60° and EF = 9 cm. Work out the exact length of DE.

14.A rectangular photograph has an area of 96 cm². One of its sides is 8 cm long. Work out the length of the other side.

15.A shape is made by joining two rectangles edge to edge, with no overlap. One rectangle measures 12 cm by 4 cm and the other measures 4 cm by 8 cm. Work out the total area of the shape.