Question

how many diagonals does a hexagon have?
______ diagonals

question 9
how many diagonals does a nonagon have?
______ diagonals

Explanation:

Step1: Recall the formula for the number of diagonals of an \(n -\)sided polygon

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

Step2: Find the number of diagonals of a hexagon

For a hexagon, \(n = 6\). Substitute \(n=6\) into the formula: \(D=\frac{6\times(6 - 3)}{2}=\frac{6\times3}{2}\).
Since \(6\times3 = 18\) and \(\frac{18}{2}=9\).

Step3: Find the number of diagonals of a nonagon

For a nonagon, \(n = 9\). Substitute \(n = 9\) into the formula: \(D=\frac{9\times(9 - 3)}{2}=\frac{9\times6}{2}\).
Since \(9\times6=54\) and \(\frac{54}{2}=27\).

Answer:

Hexagon: \(9\) diagonals
Nonagon: \(27\) diagonals