Geometry and measures worksheet — GCSE Foundation

1.A(1, 2), B(5, 2) and C(5, 6) are three of the four vertices of a square ABCD. Work out the coordinates of D.

2.A fish tank is a cuboid measuring 40 cm long, 25 cm wide and 30 cm high. Water is poured in to a depth of 20 cm. Work out the volume of water in the tank, in litres.

3.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?

4.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.

5.Write down the exact value of sin 45°.

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

7.In kite WXYZ, WX = WZ and XY = ZY (so at each of X and Z, one side from each of the two unequal pairs meets). Angle X = 100°. Work out angle Z.

8.Triangle XYZ has angle X = 90°. Angle Y = 34°. Work out angle Z.

9.Triangle ABC has AB = 6 cm, BC = 8 cm and angle B = 90°. Triangle XYZ has XY = 6 cm, YZ = 8 cm and angle Y = 90°. Which congruence statement correctly shows the matching vertices?

10.A water tank holds 2.5 m³. Work out this volume in cm³.

11.A map has a scale of 1 : 25000. A distance between two points measures 2 cm on the map. What is the real distance, in kilometres?

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

13.Two sides of a triangle are 20 cm and 8 cm long. Write down which one of these lengths is possible for the third side.

14.Angle ABC is 130°. The line BF divides angle ABC into two equal parts. Work out the size of angle FBC.

15.A right-angled triangle has angles of 90°, 40° and x°. Work out the value of x.