Regular Polygon Formulas

Posted In: Mathematics

In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex or star. We will discuss the property of regular convex polygon here.

Regular Convex Polygon


Side length: a
Number of sides: n
Internal angle: α
Slant height: m
Radius of circumscribed circle: R
Radius of inscribed circle: r
Perimeter: L
Semiperimeter: p
Area: S

  1. $α={n-2}/n\ 180°$
  2. $R=a/{2\ sin\ π/n}$
  3. $r=m=a/{2\ tan\ π/n}=√{R^2-a^2/4}$
  4. $L=na$
  5. $S=pr=p√{R^2-a^2/4},$
    $S={nR^2}/2\ sin\ {2π}/n,$
    where $p=L/2$

Post Tags: Geometry


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