Geometry and measures worksheet — GCSE Foundation

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

2.An isosceles trapezium has exactly one pair of parallel sides, and its two non-parallel sides are equal in length. How many lines of symmetry does it have?

3.A circle has two straight radii drawn from the centre to the edge, together with the arc between them. Write down the name of the region enclosed by these two radii and the arc.

4.A parallelogram has a base of 4 cm and a perpendicular height of 17 cm. Work out the area of the parallelogram.

5.Triangle T has a vertex at (8, 4). It is enlarged by a scale factor of 1/2, centre (2, 4). Work out the coordinates of the image of this vertex.

6.Write down the name given to a quadrilateral with exactly one pair of parallel sides.

7.A sector of a circle has an angle of 150°. Work out what fraction of the circle's area the sector is.

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

9.A plumber charges a £45 call-out fee, plus £28 for each hour worked. She works on a job for 3 hours 30 minutes, and her hours are billed by rounding up to the next whole hour. Work out the total amount she charges.

10.In kite WXYZ, WX = WZ and XY = ZY (so at each of X and Z, one side from each of the two unequal pairs meets). Angle X = 100°. Work out angle Z.

11.A scale model of a bridge is built so that 2 cm on the model represents 5 m of the real bridge. The real bridge is 45 m long. Work out the length of the model bridge, in centimetres.

12.A roof has two triangular sections, P and Q. Section P has a sloping edge of 3.6 m and a base edge of 2.4 m, with an angle of 70° between them. Section Q has a sloping edge of 3.6 m and a base edge of 2.4 m, with an angle of 70° between them, arranged the same way round. A roofer wants to cut identical triangular felt panels for both sections without measuring Section Q separately. Which condition confirms that the two sections are congruent?

13.A rectangular photograph has an area of 96 cm². One of its sides is 8 cm long. Work out the length of the other side.

14.Point A and point B are 5 cm apart. How many points are exactly 4 cm from A and exactly 3 cm from B?

15.Two angles lie on a straight line. One angle is 37°. Work out the size of the other angle.