Functional Skills Maths · England

Area, perimeter and volume

Measure around shapes, find the space inside them, and work out how much a container holds — from rooms and gardens at Level 1 to circles, cylinders and surface area at Level 2.

Audience
Adults & apprentices
Levels
Level 1 · Level 2 (triangles, circles, cylinders)
Worked examples
5
Format
Print (A4/Letter) + answers

Learn

Perimeter and area

Perimeter is the distance all the way round a shape, measured in units of length such as metres. Add every side, including any you have to work out from the others. Area is the amount of flat space inside, measured in square units such as m² or cm². For a rectangle, area = length × width.

Composite shapes, such as an L-shaped room, can be split into rectangles. Work out each area and add them, or find a big rectangle and subtract the missing corner. Either way, sketch it and label every length before you start.

Volume

Volume is the space inside a 3D object, measured in cubic units (cm³, m³). For a cuboid, volume = length × width × height; for a cube every side is the same, so it is side × side × side. Capacity links volume to liquid: 1,000 cm³ = 1 litre and 1 m³ = 1,000 litres. Make sure all lengths are in the same unit before multiplying.

Triangles, circles and cylinders (Level 2)

Area of a triangle = ½ × base × perpendicular height. The height must be at right angles to the base, not the sloping side.

For circles, the radius r goes from the centre to the edge and the diameter d is twice the radius. Circumference (the distance round) = π × d. Area = π × r². Use the π button on your calculator, or 3.14 if the question says so, and round sensibly at the end. A semicircle is half of a circle, so halve the area.

A cylinder is a circle stretched upwards: volume = π × r² × height. The curved surface area is the circumference times the height, 2πrh. Surface area of a cuboid is the total area of its six faces, which come in three matching pairs: 2(lw + lh + wh).

Which formulae do you need to know?

Rectangle area and cuboid volume are expected at both levels. At Level 2, learners are typically expected to know the formulae for the area of a triangle, the area and circumference of a circle, and the volume of a cylinder, while some others — for example for less common shapes — are often provided on the paper. Formula sheets differ between providers, so check your awarding body's specification and sample papers to see exactly what you must remember.

Worked example 1

Level 1: An L-shaped room is a 5 m by 4 m rectangle with a 2 m by 1.5 m corner missing. What is its floor area?

  1. Whole rectangle: 5 × 4 = 20 m².
  2. Missing corner: 2 × 1.5 = 3 m².
  3. Area: 20 − 3 = 17 m².

Answer: 17 m²

Worked example 2

Level 1: A planter is 1.2 m long, 0.5 m wide and 0.4 m deep. How much soil does it hold?

  1. Volume = length × width × height.
  2. 1.2 × 0.5 = 0.6; 0.6 × 0.4 = 0.24.

Answer: 0.24 m³

Worked example 3

Level 2: A round table top has a radius of 0.6 m. What is its area, to 2 decimal places?

  1. Area = π × r².
  2. r² = 0.6 × 0.6 = 0.36.
  3. π × 0.36 = 1.1309…
  4. Round: 1.13 m².

Answer: 1.13 m²

Worked example 4

Level 2: A cylindrical water butt has radius 0.5 m and height 1.2 m. About how many litres does it hold?

  1. Volume = π × r² × h = π × 0.25 × 1.2 = 0.9424… m³.
  2. 1 m³ = 1,000 litres, so 0.9424… × 1,000 ≈ 942 litres.

Answer: About 942 litres

Worked example 5

Level 2: The triangular gable end of a shed has a base of 6 m and a height of 2.5 m. What is its area?

  1. Area = ½ × base × height.
  2. ½ × 6 × 2.5 = 7.5.

Answer: 7.5 m²

Watch out

Common mistakes

  • Mixing up perimeter and area, or giving area in metres instead of square metres.
  • Using the sloping side of a triangle instead of its perpendicular height.
  • Using the diameter in πr²; halve it first to get the radius.
  • Multiplying lengths in different units, such as metres and centimetres.

Real life

Where you'll use this at work or home

  • Buying flooring, turf, paint or tiles for a room or garden.
  • Working out how much fencing or skirting board to order.
  • Finding the capacity of a tank, planter or skip.
  • Estimating packaging or wrapping material from surface area.

Try it

Practice sheet

Functional Skills Maths · Level 1

Area, perimeter and volume

NameDate

Show your working. Give money to the nearest penny and include units in every answer.

  1. 1.A lawn is 8 m by 5.5 m. What is its area?
  2. 2.What is the perimeter of the 8 m by 5.5 m lawn?
  3. 3.How much fencing is needed to go round a 12 m by 9 m yard?
  4. 4.How many 20 cm square tiles cover a 1 m by 0.6 m splashback?
  5. 5.A box is 30 cm by 20 cm by 15 cm. What is its volume?
  6. 6.A room is 4.5 m by 3.6 m. Carpet costs £12 per m². What does it cost to carpet?
  7. 7.A shape is made of a 6 m by 4 m rectangle and a 3 m by 2 m rectangle. What is its total area?
  8. 8.What is the volume of a cube with 5 cm sides?
  9. 9.A 5 m by 3.5 m room has a 0.9 m wide door. How much skirting board is needed?
  10. 10.A wall is 4 m by 2.5 m. One tin of paint covers 5 m². How many tins for one coat?
paperkindprintables.com

Questions

Frequently asked questions

Typically the area of a triangle, the area and circumference of a circle, and the volume of a cylinder, as well as rectangles and cuboids. Formula sheets vary, so check your awarding body's specification.

Use whatever the question asks. If it does not say, the π button is more accurate; round your final answer sensibly.

Divide by 1,000, because 1 litre = 1,000 cm³.

Draw it, split it into rectangles (and triangles or semicircles at Level 2), work out any missing lengths, then add or subtract the areas.

Next steps

Formulae and order of operationsWord formulae, BIDMAS and substitution into expressions.Scale drawings, maps and coordinatesMap scales, plans and elevations, and coordinates.Units, time and conversionsMetric units, time, imperial conversions, speed and density.All Functional Skills Maths topicsThe full learning path, Level 1 and Level 2.

Last reviewed: 9 October 2026

Editor: Paul Smeaton CMgr FCMI