Question

how many distinct diagonals does a hexagon have?_____ diagonals

Explanation:

Step1: Recall the formula for the number of diagonals

The formula for the number of diagonals \(d\) in an \(n -\)sided polygon is \(d=\frac{n(n - 3)}{2}\).

Step2: Substitute \(n = 6\) (since a hexagon has \(n=6\) sides)

Substitute \(n = 6\) into the formula: \(d=\frac{6\times(6 - 3)}{2}\).
First, calculate \(6-3=3\). Then, \(6\times3 = 18\). Finally, \(\frac{18}{2}=9\).

Answer:

\(9\)