Geometry and measures worksheet — GCSE Foundation

1.A polygon has 9 sides. What is the name of this polygon?

2.A sector of a circle has radius 7 cm and angle 90°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.

3.Which of these correctly compares a 'line' with a 'line segment'?

4.A right-angled triangle has a hypotenuse of 10 cm. One of its other angles is 45°. Work out the exact length of one of the two shorter sides.

5.The diagram shows a solid built from identical cubes. How many squares are in its plan view, the view looking straight down from above?

6.A right-angled triangle has its two shorter sides equal to 8 cm and 15 cm. Work out the value of cos θ, where θ is the angle opposite the 8 cm side. Give your answer as a fraction.

7.A parallelogram has an area of 136 cm² and a base of 17 cm. Work out the perpendicular height of the parallelogram.

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

9.Point D is at (3, 7). It is reflected in the line y = x. Work out the coordinates of the image of point D.

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

11.A solid cube has a volume of 8 cm³. Work out the length of one edge of the cube.

12.A trapezium has parallel sides of length 6 cm and 10 cm, and a perpendicular height of 4 cm. Work out its area.

13.Write down the exact value of tan 60°.

14.Triangle ABC has angle A = 40°, angle B = 65° and AB = 10 cm. Triangle DEF has angle D = 40°, angle E = 65° and DE = 10 cm. Which condition proves the two triangles are congruent?

15.A shop stacks identical storage crates in a display. The diagram shows the plan of the floor positions used, with one corner position marked. Every floor position is filled with crates stacked 3 high, except the marked corner position, which is left completely empty. Work out how many crates are used in total.