Question

Find the surface area of a regular pentagonal prism with side length 8, altitude 20, and apothem approximately 5.5

Answer 1

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.


`\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)`

recall, you have two pentagons.