# Diagonals of Polygons

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 no diagonals.

### Try it Yourself:

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