A3. Which polygon has 12 more diagonals than sides?
(A) octagon
(B) nonagon
(C) decagon
(D) hendecagon
(E) dodecagon
A3. The number of diagonals in an $n$-gon is $\frac{n(n-3)}{2}$. We write the equation $n+12=\frac{n(n-3)}{2}$, which we rearrange into the quadratic equation $n^{2}-5 n-24=0$ and factorize $(n-8)(n+5)=0$. The meaningful solution is $n=8$, so an octagon has 12 more diagonals than sides.