Geometry and measures worksheet — GCSE Foundation

1.A cylindrical drum and a cuboid box are being wrapped for a display. A shop assistant wraps only the flat faces of each item, not any curved surface. How many flat faces in total does the assistant wrap across both items?

2.Triangles ABE and CDE share the vertex E, where lines AC and BD cross at E. AE equals CE, and BE equals DE. Angle AEB and angle CED are formed as vertically opposite angles where the lines cross. Which condition proves that triangle ABE is congruent to triangle CDE?

3.A straight line crosses two parallel lines. One of the angles formed is (2x + 10)°, and the angle alternate to it is 74°. Work out the value of x.

4.A rectangle has vertices at (2, 1), (9, 1), (9, 5) and (2, 5). Work out the area of the rectangle.

5.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

6.A trapezium-shaped garden bed has parallel sides of 2.5 m and 4.5 m, and a perpendicular width of 3 m. A gardener wants to know the area of the bed before ordering topsoil. Work out the area of the garden bed.

7.A cyclist's journey from her house to the shop is represented by the column vector with top number 2 and bottom number 5, where each unit is 1 km east and 1 km north. She then cycles from the shop to the park, represented by the column vector with top number 4 and bottom number −3. What single column vector represents her journey from her house directly to the park?

8.Compasses are opened to exactly half the length of AB, and arcs are drawn centred at A and at B, to construct the perpendicular bisector of AB. Why does this fail?

9.A model car is built to a scale of 1 : 24. The real car is 4.32 m long. Work out the length of the model, in centimetres.

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

11.A drone flies from its base in three stages, each stage measured in metres east and north as a column vector. Stage 1 is the column vector with top number 30 and bottom number 40. Stage 2 is the column vector with top number −10 and bottom number 20. Stage 3 is the column vector with top number 15 and bottom number −5. Work out the column vector that would take the drone in a single straight flight back to its base from where it ends up.

12.The sum of the interior angles of a polygon is 1980°. Work out the number of sides of the polygon.

13.Triangle ABC has AB = (2x + 3) cm, BC = 11 cm and angle B = 90°. Triangle DEF has DE = 13 cm, EF = 11 cm and angle E = 90°. Given that the two triangles are congruent by SAS, work out the value of x.

14.A wooden cube has edges of length 4 cm. Work out the total surface area of the cube.

15.Two triangles are similar. The sides of the first triangle are 3 cm, 4 cm and 5 cm. The shortest side of the second triangle is 9 cm. Work out the scale factor from the first triangle to the second.