Ans: C
Let $x\text{ cm}$ be the length of the hypotenuse of the base triangle.
$\begin{array}{rcl}
x^2 & = & 5^2 +12^2 \\
& = & 169 \\
x & = & 13
\end{array}$
Therefore total surface area of the solid right triangular prism
$\begin{array}{cl}
= & 2\times \dfrac{1}{2}(5)(12) + (5+12+13)\times 20 \\
= & 660\text{ cm}^2
\end{array}$
