Perimeter, Area and VolumeEdexcel GCSE Maths: Subtopic test

1. 1
   A garden is in the shape of a rectangle measuring 12 m by 7 m. A triangular flower bed sits inside the garden with a base of 4 m and a perpendicular height of 3 m.

   (a)

   What is the perimeter, in metres, of the rectangular garden?

   [1 mark]

   • A19 m
   • B38 m
   • C42 m
   • D84 m

   (b)

   What is the area, in m², of the rectangular garden?

   [1 mark]

   • A19 m²
   • B38 m²
   • C84 m²
   • D168 m²

   (c)

   What is the area, in m², of the triangular flower bed?

   [1 mark]

   • A6 m²
   • B7 m²
   • C12 m²
   • D24 m²

   Total for question 1: 3 marks

2. 2
   A conservatory floor is made from a rectangle measuring 5 m by 3 m, joined along one edge to a trapezium-shaped section. The trapezium has parallel sides of 3 m and 5 m, and a perpendicular height of 2 m.

   (a)

   Calculate the area of the trapezium-shaped section.

   [2 marks]

   (b)

   Show that the total area of the conservatory floor is 23 m².

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A builder is laying a patio in the shape of a rectangle measuring 9 m by 6 m, with a right-angled triangular section removed from one corner. The two shorter sides of the removed triangle measure 3 m and 4 m.

   (a)

   Paving slabs cost £18 each and each slab covers exactly 1 m². Work out the total cost of the paving slabs needed to pave the patio, after the triangular section has been removed.

   [3 marks]

   (b)

   Show that the perimeter of the removed triangular section is 12 m.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A metal water tank is in the shape of a cuboid with length 2 m, width 1.5 m and height 1.2 m. Water is pumped into the empty tank at a constant rate of 0.3 m³ per minute. The tank has no lid.

   (a)

   Work out how long, in minutes, it will take to fill the tank completely.

   [4 marks]

   (b)

   Show that the total surface area of the tank, made up of the base and the four sides since there is no lid, is 11.4 m².

   [4 marks]

   (c)

   A second, cylindrical tank must hold the same volume of water as the cuboid tank, 3.6 m³. The cylindrical tank has a radius of 0.6 m. Work out the height of the cylindrical tank, giving your answer correct to 2 decimal places.

   [5 marks]

   Total for question 4: 13 marks

End of questions