How Many Diagonals Does a Decagon Have?

many-diagonals-decagon Credit: hragvartanian/CC-BY 2.0

A decagon has 35 diagonals regardless of whether it is a regular or irregular polygon. This can be determined by using a simple formula that applies to polygons with any number of sides.

A diagonal, when used in reference to polygons, is a term used to describe the number of line segments that can be connected from any one vertex to another that is already attached to it. Since each vertex is already connected to itself and the two directly beside it, diagonals can be drawn to the number of vertices in the polygon minus three. This number is then multiplied by the number of vertices and divided by two to account for each line segment having two end points. Thus the formula n(n-3)/2, where "n" is the number of vertices, calculates the number of diagonals in any given polygon.