# Regular Polygons

## Areas of regular polygons - polygons with 3 to 12 sides.

### Perimeter of a Regular Polygon

*P = n a (1)*

*where *

*P = perimeter (m, ft ..)*

*n = number of sides*

*a = length of side (m, ft, ..)*

### Area of a Regular Polygon

*A = n a r / 2*

* = n r ^{2} tan(Θ) *

* = n R ^{2} sin(2 Θ) / 2 (2)*

Polygon | Number of Sides- n - | Area(m^{2}, ft^{2} ..)^{} |
---|---|---|

Triangle, equilateral | 3 | 0.4330 a^{2} |

Square | 4 | 1.0000 a^{2} |

Pentagon | 5 | 1.7205 a^{2} |

Hexagon | 6 | 2.5981 a^{2} |

Heptagon | 7 | 3.6339 a^{2} |

Octagon | 8 | 4.8284 a^{2} |

Nonagon | 9 | 6.1818 a^{2} |

Decagon | 10 | 7.6942 a^{2} |

Undecagon | 11 | 9.3656 a^{2} |

Dodecagon | 12 | 11.1961 a^{2} |