Appendix A - A.5 - The Quadratic Formula and Square Root Properties - Exercises - Page 562: 36

The number of sides in the polygon is $~5$

We can solve the equation as follows: $\frac{n~(n-3)}{2} = D$ $\frac{n~(n-3)}{2} = n$ $n~(n-3) = 2n$ $n^2-3n = 2n$ $n^2-5n = 0$ $n~(n-5) = 0$ $n=0~~$or $~~n-5=0$ $n = 0~~$ or $~~n=5$ Since the number $n$ must be a positive number, $n=5$ The number of sides in the polygon is $~5$