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 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.