check the picture below.
notice, the prims is really just 5 rectangles, of 8x20 each, and two pentagons.
so, just get the area of the 5 rectangles, and the 2 pentagonal bases, sum them up, and that's the surface area of the pentagonal prism.
[tex]\bf \textit{area of a regular polygon}\\\\
A=\cfrac{1}{2}ans\quad
\begin{cases}
a=apothem\\
n=\textit{number of sides}\\
s=\textit{length of a side}\\
----------\\
s=8\\
n=5\\
a=5.5
\end{cases}\implies A=\cfrac{1}{2}(5.5)(5)(8)[/tex]
recall, you have two pentagons.
