Slant Edge of Square Pyramid

Volume $V = \frac{1}{3} a^2 h = 200 \implies \frac{1}{3} a^2 (13) = 200 \implies a^2 = \frac{600}{13}$. Distance from center of base to a vertex $d = \frac{a}{\sqrt{2}}$. So $d^2 = \frac{a^2}{2} = \frac{300}{13}$. Slant edge $e = \sqrt{h^2 + d^2} = \sqrt{13^2 + \frac{300}{13}} = \sqrt{169 + 23.0769} = \sqrt{192.0769} \approx 13.86 \text{ cm}$. Rounded to nearest integer, $e = 14$ cm.