# Polygon

A polygon is a union of disjoint line segments that is connected.

A regular polygon has all sides equal and all angles equal.

Types, by number of sides.

1. There is no such mathematical entity as a one sided polygon in a plane. (For higher dimensional analogies, see Mobius strip and Klein bottle.)
2. As with the one-sided polygon, there is no such thing as a two-sided polygon. (This would be two overlapping line segments.)
3. Triangle - three sided, see isosceles triangle, equilateral triangle, right triangle
5. Pentagon - five sided. The most famous one houses the Department of Defense.
6. Hexagon - six sided, the shape of a bee hive cell, also used in some board games
7. Heptagon - seven sided. Some coins have been been heptagonal.
8. Octagon - eight sided, used for stop signs in the U.S.
9. Higher orders of polygons are: nonagon (9-sided), decagon (10-sided), unodecagon (11-sided), duodecagon (12-sided) etc.
10. Polygons of higher orders than the duodecagon are often named n-gons, where n is the amount of its sides. For example, a 42-gon would be a polygon with 42 sides.

## Formulas

The perimeter of a regular polygon is equal to $n sin\frac{180}{n} (2) (r)$, where r equals the length of the radius.
The area of a regular polygon is equal to $n sin\frac{180}{n}cos\frac{180}{n}(r^2)$