Appears in: Functional Skills Level 1 · Functional Skills Level 2 · GCSE foundation
Area and perimeter: how to work them out
Area is how much surface a shape covers; perimeter is the distance around its edge. Functional Skills tends to ask about real things — turfing a lawn, fencing a garden, tiling a floor — and GCSE foundation adds circles and compound shapes. The formulas are few, and the marks are mostly lost on units and on missing a side.
The formulas
- Rectangle: area = length × width; perimeter = 2 × (length + width).
- Triangle: area = ½ × base × height, where the height is measured at right angles to the base.
- Trapezium: area = ½ × (a + b) × h, where a and b are the two parallel sides.
- Circle: area = π × r²; circumference = π × d (or 2 × π × r). Use the π button, and give the units.
- Compound shapes: split into rectangles and add, or find a big rectangle and subtract the missing piece. For perimeter, go round the outside and count every edge — including the ones you had to work out.
- Area is in square units (m², cm²); perimeter is in ordinary units (m, cm).
Worked examples
Example 1
A rectangular lawn is 12 m by 7.5 m. Turf costs £4.20 per m². How much does turfing it cost?
- Area = 12 × 7.5 = 90 m².
- Cost = 90 × £4.20 = £378.
Example 2
Work out the area of a triangle with base 10 cm and height 6 cm.
- Area = ½ × 10 × 6 = 30 cm².
Example 3
A trapezium has parallel sides of 6 cm and 10 cm and a height of 4 cm. Find its area.
- Area = ½ × (6 + 10) × 4 = ½ × 16 × 4 = 32 cm².
Example 4
An L-shaped room is a 10 m by 6 m rectangle with a 4 m by 3 m corner missing. What is its floor area?
- Whole rectangle: 10 × 6 = 60 m².
- Missing corner: 4 × 3 = 12 m².
- Floor area = 60 − 12 = 48 m².
Example 5
A circular pond has a radius of 4 m. Work out its area to one decimal place.
- Area = π × 4² = π × 16.
- = 50.3 m² (to 1 d.p.).
Where the marks go missing
- Using the slanted side of a triangle as its height. The height is the perpendicular distance from the base.
- Squaring the diameter instead of the radius in π r². Halve the diameter first.
- Adding only the sides you were given for a compound-shape perimeter. Work out the missing lengths and include every edge.
- Writing m instead of m² for an area, or the other way round.
Frequently asked questions
What is the difference between area and perimeter?
Perimeter is the total length around the outside of a shape, measured in cm, m and so on. Area is the amount of surface inside it, measured in square units like cm² or m².
How do you work out the area of a circle?
Multiply π by the radius squared: area = π r². For a radius of 5 cm, that's π × 25 ≈ 78.5 cm².