Regular polygon

A regular polygon is a polygon that is cyclic and equilateral.

The taxonomic classification of polygons is illustrated by the following graph:

                                      Polygon
                                     /       \
                                 Simple     Complex
                                /      \      /
                           Convex    Concave /
                            /    \     /    /
                       Cyclic    Equilateral
                           \     /    
                           Regular

For each number of sides, all regular polygons with that number of sides are similar.

The regular polygons most commonly found include:

• Equilateral triangle
• Square
• Regular pentagon
• Regular hexagon
• Regular octagon

Somewhat less common are:

• Regular decagon
• Regular dodecagon

Area

File:Apothem of hexagon.png

Apothem of a hexagon

The area of a regular n-sided polygon is

$A={\frac {nt^{2}}{4\tan(\pi /n)}}$

where t is the length of a side, or half the perimeter multiplied by the length of the apothem (the line drawn from the centre of the polygon perpendicular to a side)

For n=2,3,4,5,6 and t=1 this gives 0, 0.433, 1, 1.720, 2.598, respectively.

See also

• tilings of regular polygons

External links

• Mathworld: Regular Polygon