Geometry and measures worksheet — GCSE Foundation

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

2.A garden designer describes a flower bed as a shape with four straight sides: exactly one pair of sides is parallel, those two parallel sides are different lengths, and the other two sides are equal in length to each other but not parallel to each other. Which shape should the designer draw?

3.A shopkeeper builds a display from two cuboid boxes, shown in the diagram. She wants to cover the front of the display with coloured paper. Work out the total area of the front elevation, in square centimetres.

4.A solid has 10 vertices and 15 edges. Using the formula F + V − E = 2, work out how many faces it has.

5.A parallelogram has an area of 54 cm² and a base of 9 cm. Work out its perpendicular height.

6.To construct the perpendicular from a point P to a line l, where P is a point above l, an arc centred at P is drawn to cross l at two points, X and Y. What is the correct next step?

7.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.

8.The perimeter of a square is 20 cm. Work out the area of the square.

9.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.

10.Two triangles are congruent to each other. What does this tell you about their angles and sides?

11.Work out the exact value of tan 30° + tan 30°.

12.A rectangle has vertices A(0, 0), B(6, 0), C(6, 4) and D(0, 4). Work out the length of the diagonal AC. Give your answer correct to 2 decimal places.

13.A church tower is due east of a village. What is the three-figure bearing of the church tower from the village?

14.In quadrilateral ABCD, side AB is parallel to side DC. Which statement correctly uses geometric notation to show this?

15.A footpath is 3750 m long. Work out this distance in kilometres.