Diagonals Of Polygons - Math Is Fun

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Diagonals of Polygons

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

A square has 2 diagonals

An octagon has 20 diagonals

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

n(n − 3) / 2

Why does this work?

Each of the n corners joins to (n − 1) other corners
Two of those are edges, so there are (n − 3) diagonals from each corner
That seems like n(n − 3) diagonals, but each diagonal is counted twice (once from each end),
so we divide by 2: n(n − 3) / 2

images/area-coords.js?mode=diag

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