Area and perimeter: how to choose the right formula
Use the question and units to distinguish a shape's boundary from the space it covers.
In this guide
Quick answer
Perimeter is the total length around a shape; area measures the surface inside it. For a rectangle use P = 2(a + b) and A = a × b, and keep linear units separate from square units.
Before calculating, sketch the figure and label the known sides. A simple diagram helps you see whether the question asks for a boundary, an unknown length or a surface.
Rectangle with known sides
A rectangle is 8 cm long and 5 cm wide. Its perimeter is 2(8 + 5) = 26 cm. Its area is 8 × 5 = 40 cm². The same dimensions give two different quantities because the questions are different.
Recover a missing side
A rectangle has area 63 cm² and width 7 cm. Since A = a × b, its length is 63 ÷ 7 = 9 cm. Now its perimeter is 2(9 + 7) = 32 cm.
Dividing the area by a known side recovers a length. Adding the area to a side does not have a meaningful unit here.
A triangle needs its height
A triangle with base 10 cm and perpendicular height 6 cm has area 10 × 6 ÷ 2 = 30 cm². The height must be perpendicular to the chosen base; an arbitrary sloping side is not a substitute.
Check the units and the question
Write cm for a length and cm² for an area. Convert measurements to the same unit before using a formula. Practise with the mathematics examples, and keep a diagram and explanation in notes when a formula choice is unclear.
Sources and further reading
Reference material supports the explanations.
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