# The Polygon

Polygon is a closed plane figure bounded by straight lines. There are two basic types of polygons, a convex and a concave polygon. Polygon is said to be convex if no side when extended will pass inside the polygon, otherwise it is concave.

**Name of Polygons**

No. of Sides, n |
Name |

1 | Monogon, Henagon (cannot exist) |

2 | Digon (cannot exist) |

3 | Triangle, Trigon |

4 | Quadrilateral, Quadrangle, Tetragon |

5 | Pentagon |

6 | Hexagon |

7 | Heptagon, Septagon |

8 | Octagon |

9 | Nonagon, Enneagon |

10 | Decagon |

11 | Undecagon, Hendecagon |

12 | Dodecagon, Duodecagon |

13 | Tridecagon, Triskaidecagon |

14 | Tetradecagon, Tetrakaidecagon |

15 | Pentadecagon, Quindecagon, Pentakaidecagon |

16 | Hexadecagon, Hexakaidecagon |

17 | Heptadecagon, Heptakaidecagon |

18 | Octadecagon, Octakaidecagon |

19 | Enneadecagon, Ennekaidecagon, Nonadecagon |

20 | Icosagon |

30 | Triacontagon |

40 | Tetracontagon |

50 | Pentacontagon |

70 | Heptacontagon |

80 | Octacontagon |

90 | Enneacontagon |

100 | Hectogon |

1000 | Chilliagon |

10 000 | Myriagon |

1 000 000 | Megagon |

**The following are true for convex polygon**

- The sum of the angles of polygon of n sides is 180°(n - 2) right angles.
- The exterior angles of a polygon are together equal to 4 right angles.

**Formulas for convex polygon**

$\Sigma \beta = 180^\circ (n - 2)$

$\Sigma \alpha = 360^\circ$

$D = \dfrac{n}{2}(n - 3)$