Geometry and measures worksheet — GCSE Foundation

1.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?

2.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.

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 locus consists of all the points that are the same perpendicular distance from two parallel lines 6 cm apart. Describe this locus.

5.A recipe uses 0.75 kg of sugar. Work out how many grams of sugar this is.

6.A path goes from A(1, 1) to B(1, 5), then from B to C(6, 5). Work out the total length of the path from A to C.

7.A parallelogram has a base of 20 cm and a sloping side of 13 cm. The perpendicular drawn from the top of that sloping side down to the base meets the base 5 cm from the foot of the sloping side, so the perpendicular, the 5 cm and the 13 cm sloping side form a right-angled triangle. Work out the area of the parallelogram.

8.A bottle holds 2 litres of water. A glass holds 250 ml. Work out how many of these glasses can be filled from one full bottle.

9.The point (2, 5) is translated 3 units right and 4 units down. Work out the coordinates of the image point.

10.A rectangle has vertices at (2, 1), (9, 1), (9, 5) and (2, 5). Work out the area of the rectangle.

11.A bus journey takes 2.5 hours. Work out how many minutes this is.

12.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).

13.In one circle, chord PQ is 6 cm long, chord RS is 10 cm long, chord TU is 14 cm long and chord VW is 15 cm long. Write down which of these chords lies closest to the centre of the circle.

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

15.A rectangular gate is braced with a diagonal strut. The gate is 1.2 m wide and 0.9 m tall. Work out the exact length of the diagonal strut.