Number of Diagonals of a Polygon

The number of diagonals in a polygon with $n$ vertices (an n-gon) can be calculated with a simple formula. From each of the $n$ vertices, you can draw $(n-3)$ diagonals. Since each diagonal is counted twice with this method (once for each endpoint), the total number of distinct diagonals is:

Number of Diagonals = $\frac{n(n-3)}{2}$

For example, in a hexagon ($n=6$), the number of diagonals is $\frac{6(6-3)}{2} = \frac{6 \times 3}{2} = 9$.