Question

Find the number of diagonals of a hexagon

Answer 1

A diagonal connects two non-consecutive vertices of a polygon

A hexagon has six sides.

There are $3$ diagonals from a single vertex, and there are $6$ vertices on a hexagon, which suggests there would be $18$ diagonals in a hexagon.

However, we must divide by two as half of the diagonals are common to the same vertices, Thus there are $9$ unique in a hexagon.

The formula for the number of diagonals of a polygon is

$\frac{n(n-3)}{2}\Rightarrow n=$ number of sides of a polygon $\Rightarrow \frac{6(6-3)}{2}\Rightarrow 9$