Geometry and measures worksheet — GCSE Foundation

1.A parallelogram has a base of 9 cm and a perpendicular height of 4 cm. Work out its area.

2.The three angles of a triangle are 10°, 58° and 112°. Write down the name that describes this triangle.

3.In triangle ABC and triangle DEF, AB = DE, AC = DF, and the angle at A equals the angle at D. Write down the congruence condition that proves the two triangles are congruent.

4.The midpoint of the line segment AB is (3, 5). A is the point (1, 3). Work out the coordinates of B.

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

6.Write down the column vector, from the options given, that would move a point to the right and downwards.

7.A garden bed is designed as a trapezium. The two parallel sides are 8 m and 12 m, and the perpendicular distance between them is 5 m. Grass seed covers 4 m² per bag, sold only in whole bags. Work out how many bags of grass seed are needed.

8.A chocolate bar is a prism. Its cross-section is a triangle with a base of 6 cm and a perpendicular height of 5 cm, and the bar is 12 cm long. Work out the volume of the bar.

9.In triangle ABC the angle at A is 90° and BC = 10 cm. For the angle at B, sin B = 3/5. Work out the length of AC.

10.A scale drawing of a bridge uses a scale of 1 : 25. A support beam on the drawing measures 4.4 cm. What is the real length of the beam, in metres?

11.Two sides of a triangle are 9 cm and 15 cm long. Write down which one of these lengths is possible for the third side.

12.A tank holds 3.2 m³ of water. Work out this volume in litres.

13.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.

14.Work out the exact value of sin 45° × cos 45°.

15.A circle has circumference 31.4 cm. Using π = 3.14, work out the radius of the circle.