Geometry and measures worksheet — GCSE Foundation

1.A plan of a car park is drawn to a scale of 1 : 500. A parking bay is drawn as a rectangle measuring 1.2 cm by 0.6 cm. The real width of the bay corresponds to the 0.6 cm side. What is the real width of the bay, in metres?

2.In a right-angled triangle, the two shorter sides are a and b, and the hypotenuse is c. Write down the correct statement of Pythagoras' theorem.

3.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.

4.A patio plan states: 'Side AB of the patio is parallel to side DC, and AB is longer than DC. Sides BC and AD are not parallel to each other and are not equal in length.' The four sides measure AB = 5.1 m, BC = 3.2 m, DC = 2.8 m and AD = 4.5 m. The tiler needs to order edging strip only for the sides that are not parallel to any other side. What total length of edging strip, in metres, should the tiler order?

5.The interior angles of a pentagon are 100°, 110°, 120°, x° and x°. Work out the size of each of the two angles marked x°.

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

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

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

9.In this question, a curved surface counts as a face. How many faces does a cone have?

10.A ship's radio can be heard up to 30 km from the ship. A lighthouse's light can be seen up to 20 km from the lighthouse. The ship and the lighthouse are 40 km apart along the coast. Describe the region where BOTH the radio can be heard AND the light can be seen.

11.Triangle PQR and triangle XYZ have angle P = angle X, angle Q = angle Y and angle R = angle Z, with no side lengths given for either triangle. Which of the following correctly describes the relationship between the two triangles?

12.A cube has all of its edges the same length. How many planes of symmetry does it have?

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

14.A chord divides a circle into two segments of different sizes. Write down the name given to the smaller of the two segments.

15.Write down the name given to a quadrilateral that has exactly one pair of parallel sides.