Geometry and measures worksheet — GCSE Foundation

1.How many vertices does a cuboid have?

2.The point (4, −3) is reflected in the y-axis. Work out the coordinates of the image point.

3.Point B is at (1, 6). It is reflected in the x-axis. Work out the coordinates of the image of point B.

4.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.

5.A triangular bunting flag has two equal sides. The angle between those two equal sides is 80°, and the other two angles of the flag are equal to each other. Work out the size of each of the two equal angles.

6.A sector of a circle has radius 10 cm and angle 72°. Using π = 3.14, work out the arc length of the sector.

7.A solid pyramid has a square base of side 10 cm and four identical triangular faces. Its apex is directly above the centre of the base, at a vertical height of 12 cm, and the slant height of each triangular face — the distance from the apex to the midpoint of a base edge — is 13 cm. Work out the total surface area of the pyramid.

8.A sector of a circle has radius 9 cm and angle 40°. Work out the area of the sector, in terms of π.

9.A trapezium has parallel sides of 16 cm and 24 cm, and a perpendicular height of 7 cm. Work out the area of the trapezium.

10.A solid has a plan view that is a circle, and a front elevation that is a triangle. Which solid is this?

11.In an isosceles triangle each of the two base angles is 46°. Work out the size of the angle at the apex.

12.The column vector r has top number 2 and bottom number 6. Which of these column vectors is parallel to r?

13.The diagram shows the plan view and the front elevation of a cuboid-shaped box, each drawn as a rectangle. Work out the area of the box's side elevation, in square centimetres.

14.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.

15.A shape is made by joining two rectangles edge to edge, with no overlap. One rectangle measures 12 cm by 4 cm and the other measures 4 cm by 8 cm. Work out the total area of the shape.