2.2.4 Number of Diagonals of a Polygon

The formula for the number of diagonals in a polygon is derived by noticing that from each of the $n$ vertices in an $n$-gon, you can draw $(n - 3)$ diagonals creating $n(n - 3)$ diagonals, however each diagonal would be drawn twice, so the total number of diagonals is:

\text{# of Diagonals} = \frac{n(n - 3)}{2}

Example: Find the number of diagonals in a hexagon ($n=6$). \text{# of Diagonals} = \frac{6(6 - 3)}{2} = \frac{6 \cdot 3}{2} = 9

Problem Set 2.2.4