Geometry and measures worksheet — GCSE Foundation

1.A map has a scale of 1 cm : 5 km. A road is drawn 3 cm long on the map. What is the real length of the road?

2.The three angles of a triangle are 10°, 58° and 112°. Write down the name that describes this triangle.

3.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.

4.Two straight lines PQ and RS cross at point O. Angle POR = 52°. Work out angle QOS.

5.A circle has a radius of 3 cm. Work out the diameter of the circle.

6.Two similar ponds have perimeters in the ratio 4 : 11. The perimeter of the larger pond is 88 m. Work out the perimeter of the smaller pond.

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

8.Triangle ABC has a right angle at B and hypotenuse AC = 17 cm, with AB = 8 cm. Triangle DEF has a right angle at E and hypotenuse DF = 17 cm. Which extra fact about DEF would complete the RHS condition for proving that ABC ≅ DEF, with the vertices matching in that order?

9.Vertex X of a triangle is at (−3, 5). After a translation, the image of X is at (2, −1). Write down the column vector of this translation.

10.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.

11.The angle between north and a cycle path is 40°, but it is measured anticlockwise from north. What is the three-figure bearing of the cycle path?

12.A parallelogram has an area of 96 cm² and a base of 8 cm. Work out the perpendicular height of the parallelogram.

13.A solid has 4 triangular faces, 4 vertices and 6 edges. What is the name of this solid?

14.u is the column vector with top number 7 and bottom number 3. v is the column vector with top number 2 and bottom number 5. Work out u − v, giving your answer as a column vector in the form (top, bottom).

15.Work out the exact value of sin 30° + cos 60°.