Geometry and measures worksheet — GCSE Foundation

1.A garden water trough is a prism whose cross-section is a right-angled triangle with base 40 cm and height 30 cm. The trough is 120 cm long. Work out the volume of water needed to fill the trough completely.

2.The diagram shows a prism resting on a table. Which shape is its front elevation, the view looking at it from directly in front?

3.A roof truss has two horizontal parallel rafters, one above the other. A straight strut crosses both rafters. Where the strut crosses the lower rafter, the angle above the rafter and to the left of the strut is 65°. Work out the size of the angle above the upper rafter and to the right of the strut, where the strut crosses it.

4.Work out the distance between the point (0, 0) and the point (5, 12).

5.A translation moves the point (1, 1) to the point (9, 4). Write down the column vector of this translation.

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

7.A parallelogram has a base of 9 cm and a perpendicular height of 6 cm. Work out the area of the parallelogram.

8.Point D is at (3, 4). It is rotated 90° clockwise about the origin (0, 0). Work out the coordinates of the image of point D.

9.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.

10.A sector of a circle has an angle of 90° at the centre. Write down what fraction of the whole circle this sector represents.

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.A square has sides of length 7 cm. Work out its area.

13.A dog is tied by a lead 4 m long to a fixed ring on a straight garden wall. The wall extends much further than the lead can reach in both directions, and the dog cannot cross through it. Describe the region the dog can reach.

14.A jug holds 750 ml of water. Work out what fraction of a litre this is.

15.Triangle XYZ has angle X = 90°. Angle Y = 34°. Work out angle Z.