Geometry and measures worksheet — GCSE Foundation

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

2.Triangle JKL has a right angle at K, hypotenuse JL = 13 cm, and side JK = 5 cm. Triangle MNO has a right angle at N, hypotenuse MO = 13 cm, and side MN = 5 cm. Using only the facts given, and without working out any further lengths, write down the congruence condition that proves triangle JKL is congruent to triangle MNO.

3.A water tank is a cube with edges of length 2 m. Work out how many cubic centimetres the tank holds when it is full.

4.A solid has 5 faces, 9 edges and 6 vertices. Two of its faces are triangles and the other three are rectangles. Which solid is it?

5.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?

6.A solid has 5 faces: one square face and four triangular faces, which all meet at a single point above the square. What is the name of this solid?

7.Point C is at (5, 2). It is reflected in the x-axis. Work out the coordinates of the image of point C.

8.A circular plate has a diameter of 20 cm. Work out the area of the plate. Use π = 3.14.

9.How many vertices does a cylinder have?

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

11.In the RHS congruence condition, which three facts must be true about two triangles for RHS to prove they are congruent?

12.A student draws a net using 5 identical squares arranged in a row of four with one extra square attached to the side of one of them. Can this net be folded to make a closed cube?

13.A gardener wants to plant a tree so that it is the same distance from two straight garden walls that meet at a corner, and also the same distance from two ornamental posts standing 4 m apart. Which construction locates this point?

14.m is the column vector with top number 4 and bottom number 6. n is the column vector with top number −6 and bottom number −9. Given that n = k × m for some number k, work out the value of k.

15.Which of the following is the correct definition of a regular polygon?