Answer
$n = 6$
Work Step by Step
$D = \frac{n(n-3)}{2}$
$D = \frac{n^{2}-3n}{2}$
$9 = \frac{n^{2}-3n}{2}$
$18 = n^{2}-3n$
$n^{2} - 3n - 18 = 0$
Find two numbers that can be multiplied together to get $-18$ and can be added together to get $-3$.
$= 3$ and $-6$
$n^{2} + 3n - 6n - 18 = 0$
$n(n + 3) - 6(n+3) = 0$
$(n-6)(n+3) = 0$
$n = 6, -3$
Since the number of sides cannot be a negative number, then $n = 6$.