Geometry and measures worksheet — GCSE Foundation

1.A rectangular notice board measures 150 cm by 80 cm. Work out its area in m².

2.Write down which one of these quadrilaterals always has diagonals that are equal in length and that cross at right angles.

3.A designer enlarges a drawing of a model car for a poster. She first enlarges the drawing by a scale factor of 1.5, and then enlarges that result by a further scale factor of 2. On the original drawing, the position of a wheel relative to the front bumper is given by the column vector with top number 4 and bottom number −3, in centimetres. What is the corresponding column vector on the poster, in centimetres?

4.A triangular badge has two sides of length 8 cm and a third side of length 5 cm. Work out the perimeter of the badge.

5.The point (0, −5) lies on one of the two coordinate axes. Write down which axis this is.

6.P is the point (3, 4) and Q is the point (6, 0). Work out the distance of each point from the origin, and write down which point is closer to the origin.

7.A polygon has one more side than a heptagon. What is the polygon called?

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

9.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.

10.A triangle has vertices A(0, 0), B(10, 0) and C(5, 12). Work out the area of the triangle.

11.A textbook contains the instruction 'Draw AB' and, on the next line, the statement 'AB = 5 cm'. Which statement about the notation AB is correct?

12.What does the statement AB = CD mean, where A, B, C and D are all points?

13.Triangle A has a vertex at (1, 2). Triangle A is enlarged, centre (1, 1), to give triangle B, whose corresponding vertex is at (1, 5). Work out the scale factor of the enlargement.

14.A treasure map has a scale of 1 cm to 4 m. A path from the start to a rock is drawn as two straight sections, measuring 3 cm and 2.5 cm. Work out the total real distance from the start to the rock, in metres.

15.A scale drawing of a park uses a scale of 1 : 2000. A path is drawn 8.5 cm long on the drawing. A cyclist rides the length of the path and then rides straight back again along the same path. How far does the cyclist travel in total, in metres?