Perimeter of Regular Polygon

Theorem

Let $P$ be a regular $n$-sided polygon whose side length is $b$.

Then the perimeter $L$ of $P$ is given by:

$L = n b$

Proof

By definition, an $n$-sided polygon has $n$ sides.

By definition, a regular polygon has sides all the same length.

By definition, the perimeter of a polygon is the total length of all its sides.

Thus $P$ has $n$ sides all of length $b$.

Hence $L = n b$.

$\blacksquare$

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 4$: Geometric Formulas: $4.10$