Perimeter

Boundary, not interior

Imagine walking once around a garden’s edge. The distance travelled is its perimeter. Area measures the interior surface instead, so perimeter uses linear units such as metres, while area uses square metres.

The general method is dependable for every polygon: identify every outside edge and add its length exactly once.

Common formulas

For a rectangle of length $l$ and width $w$,

For a square with side $s$, $P=4s$. A regular $n$-gon with side length $s$ has $P=ns$. Formulas compress repeated addition; they do not replace understanding which edges form the boundary.

A rectangle example

The measurement answer is $29$ m; the purchasing decision requires an additional interpretation.

Units and precision

All lengths must use the same unit before addition. Convert $2.4$ m and $85$ cm to either metres or centimetres, not a mixture. Measurement precision also matters; a perimeter calculated from rounded dimensions is itself approximate.

Common mistakes

Using an area formula. Perimeter adds boundary lengths and stays in linear units.

Counting interior lines. Only the outside edge counts unless the situation says otherwise.

Missing an unlabelled side. Use shape properties and aligned totals to infer it.

Mixing units. Convert first, then add.

Quick self-check

• Have I traced one complete trip around the boundary?
• Is every outside segment counted once?
• Are all measurements in the same linear unit?
• Is the result reasonable compared with the figure’s dimensions?