Answer
$n = 5$ sides.
Work Step by Step
$D = \frac{n(n-3)}{2}$
$n = \frac{n(n-3)}{2}$
$2n = n(n-3)$
$2n = n^{2} - 3n$
$n^{2} - 3n = 2n$
$n^{2} - 3n -2n= 0$
$n^{2} - 5n = 0$
$n(n-5) = 0$
$n = 0, 5$
A polygon cannot have $0$ sides, so therefore $n = 5$ sides.