Number of Diagonals of a Polygon

Number of Diagonals of a Polygon

## Formula

A polygon with $$n$$ vertices has:

$$\frac{n(n-3)}2$$

diagonals.

## Derivation Formula

The number of line segments joining pairs of vertices is:

$${}^nC_2$$

Subtracting the $$n$$ sides:

$$\text{Diagonals}={}^nC_2-n=\frac{n(n-3)}2$$

## Usage

- Used in geometry-based counting problems involving vertices and diagonals.