# Diagonals of Polygons

A square has 2 diagonals |
An octagon has 20 diagonals |

A polygon's **diagonals** are line segments from one corner to another (but not the sides).

The number of diagonals of an n-sided polygon is:

n(n − 3) / 2

### Examples:

- a square (or any quadrilateral) has 4(4−3)/2 = 4×1/2 =
**2**diagonals - an octagon has 8(8−3)/2 = 8×5/2 =
**20**diagonals. - a triangle has 3(3−3)/2 = 3×0/2 =
**0**diagonals.

### Try it Yourself:

A diagonal can actually be outside the polygon, which happens with some concave polygons. |