Geometry and measures worksheet — GCSE Foundation

1.To construct the perpendicular from a point P to a line l, where P is a point above l, an arc centred at P is drawn to cross l at two points, X and Y. What is the correct next step?

2.Lines PQ and RS are parallel. A straight line crosses PQ at point X and crosses RS at point Y. Angle PXY = 63°. Angle PXY and angle XYS are co-interior (allied) angles, which add up to 180°. Work out the size of angle XYS.

3.A triangular prism has a cross-section that is a triangle with a base of 3.5 cm and a perpendicular height of 4 cm. The prism is 10 cm long. Work out the volume of the prism.

4.Triangle ABC has AB = 9 cm, BC = 6 cm and angle A = 35°. Triangle DEF has DE = 9 cm, EF = 6 cm and angle D = 35°. Which of the following correctly identifies the condition shown here?

5.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.

6.Quadrilateral WXYZ has WX parallel to ZY, and WZ = XY (the two non-parallel sides are equal in length). Give a reason why angle W = angle X.

7.A circular clock face has a diameter of 18 cm. Work out the circumference of the clock face. Use π = 3.14.

8.A triangle has vertices A(0, 0), B(10, 0) and C(5, 12). Work out the area of the triangle.

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

10.A rectangular notice board measures 150 cm by 80 cm. Work out its area in m².

11.A chord is drawn across a circle, dividing the circle into two regions. Write down the name of one of these two regions.

12.A regular hexagon is divided into six identical triangles by joining its centre to each of the six vertices. Work out the size of the angle of one of these triangles at the centre of the hexagon.

13.A triangle has a base of 8 cm and a perpendicular height of 5 cm. Work out its area.

14.A carpenter measures two triangular braces. Brace 1 has a 55° angle, a 65° angle, and, opposite the 55° angle, a side of 8 cm. Brace 2 has matching 55° and 65° angles and, opposite its 55° angle, a side of 8 cm. The carpenter says that because the equal 8 cm side is not between the two equal angles in either brace, he cannot be sure the two braces are the same size. Is the carpenter correct?

15.A bus journey takes 2.5 hours. Work out how many minutes this is.