Geometry and measures worksheet — GCSE Foundation

1.The diagram shows a cuboid. Work out the area of its front elevation, in square centimetres.

2.Two similar triangles have lengths in the ratio 3 : 4. The perimeter of the smaller triangle is 24 cm. Work out the perimeter of the larger triangle.

3.Write down the column vector that describes a translation of 4 units to the right and 4 units up.

4.A tangent to a circle touches the circle at exactly one point, P. Work out the size of the angle between the tangent and the radius drawn to P.

5.In triangle ABC, angle A is 2x°, angle B is 3x° and angle C is 4x°. Work out the size of angle B.

6.A running track has a straight section and a semicircular bend. The bend is a semicircle with radius 32 m. Work out the length of the curved part of the bend, to 1 decimal place. (Use π = 3.14.)

7.A solid is built from centimetre cubes standing on a table. Seen from the front, the left-hand column is 2 cubes high, the middle column is 2 cubes high and the right-hand column is 1 cube high. Work out how many squares make up the front elevation.

8.Here are four trigonometric ratios of special angles. Write down the one that does not have a value.

9.A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 20 cm. Work out the length of the other shorter side.

10.In quadrilateral ABCD the two sides AB and BC are each 6 cm long and meet each other at B. The two sides CD and DA are each 9 cm long and meet each other at D. No side of ABCD is parallel to any other side. Write down the mathematical name of this quadrilateral.

11.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?

12.Triangle T has a vertex at (8, 4). It is enlarged by a scale factor of 1/2, centre (2, 4). Work out the coordinates of the image of this vertex.

13.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.

14.p is the column vector with top number 4 and bottom number −3. Work out 2p, giving your answer as a column vector in the form (top, bottom).

15.A fan-shaped rug is in the shape of a sector of a circle with radius 4 m and angle 180°. It costs £4 per square metre to make. Using π = 3.14, work out the total cost of the rug.