Mensuration and calculation: know and apply formulae to calculate: area of triangles, parallelograms, trapezia; volume of cuboids and other right prisms (including cylinders)

The idea

This row requires you both to know and to apply mensuration formulae. For area: a triangle uses half base times perpendicular height; a parallelogram uses base times perpendicular height; a trapezium uses half the sum of the parallel sides times the perpendicular height. For volume: a cuboid uses length × width × height; any right prism uses cross-sectional area × length, and a cylinder is a right prism whose cross-section is a circle, so its volume is πr²h. Always identify the perpendicular height, not a slanted edge, and keep all lengths in the same unit before calculating.

For example: A trapezium with parallel sides 6 cm and 10 cm and perpendicular height 4 cm has area ½ × (6 + 10) × 4 = 32 cm².

What earns the marks

• Area of a triangle = ½ × base × perpendicular height, using the perpendicular height rather than a slanted side.
• Area of a parallelogram = base × perpendicular height.
• Area of a trapezium = ½ × (sum of the parallel sides) × perpendicular height.
• Volume of a cuboid = length × width × height.
• Volume of any right prism = cross-sectional area × length, applied consistently to the named solid.
• Volume of a cylinder = πr²h, treating the circular cross-section as the prism face.

Common mistakes and how to put them right

• Using a slanted side as the height.

  Put it right: The height must be perpendicular to the base, so identify the perpendicular distance before substituting.

• Forgetting the half in the triangle or trapezium formula.

  Put it right: Both require the factor ½, so check the formula before calculating.

• Mixing units, such as centimetres and metres, in one calculation.

  Put it right: Convert all lengths to a common unit first, then state the area in square units or the volume in cubic units.

• Treating the diameter as the radius in a cylinder.

  Put it right: Halve the diameter to obtain the radius before using πr²h.

Exam tips

• Write the formula you are using before substituting numbers, so the method is visible and any slip is easier to spot.
• Label the perpendicular height on a diagram before calculating, especially for triangles and trapezia.
• Check the unit of the answer: area in square units such as cm², volume in cubic units such as cm³.
• For a composite or unfamiliar right prism, find the cross-sectional area first, then multiply by the length.