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: Regular Polygon of $n$ Sides Each of Length $b$: $4.10$
  • 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 7$: Geometric Formulas: Regular Polygon of $n$ Sides Each of Length $b$: $7.10.$
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