Geometry and measures worksheet — GCSE Foundation

1.A cone is cut by a flat plane parallel to its circular base, partway up between the base and the apex. What shape is the cross-section?

2.In geometry, which of the following best describes a 'plane'?

3.In this question, a curved surface counts as a face. How many faces does a sphere have?

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 the plan view and the front elevation of a cuboid-shaped box, each drawn as a rectangle. Work out the area of the box's side elevation, in square centimetres.

6.A triangular prism has two triangular end faces and three rectangular faces joining them. How many faces does it have in total?

7.Quadrilateral WXYZ has WX parallel to ZY, and WZ = XY (the two non-parallel sides are equal in length). Give a reason why angle W = angle X.

8.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.

9.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?

10.A square tile has sides of length 4.5 cm. Work out the perimeter of the tile.

11.A rectangular garden bed measures 5 m by 3 m. A semicircular flower border is attached along one of the 3 m-wide ends, on the outside of the rectangle, so that the 3 m side is the diameter of the semicircle. Work out the total perimeter of the combined shape (the two long sides, the one remaining short side, and the curved edge). Use π = 3.14.

12.A rhombus has all four sides equal in length. Write down how many pairs of parallel sides a rhombus has.

13.A sector of a circle has radius 6 cm and an arc length of 15.7 cm. Using π = 3.14, work out the angle of the sector.

14.Write down the exact value of sin 60°.

15.Triangle ABC has a right angle at B. Triangle DEF has a right angle at E. The hypotenuse of triangle ABC equals the hypotenuse of triangle DEF, and side AB equals side DE. Which condition proves that the two triangles are congruent?