Question

What is the difference between the lateral and total surface areas of the prism sitting on its base?

Answer 1

Check the picture below.

well, firstly let's find out the areas, and then let's get their difference

`\stackrel{\textit{\LARGE total surface area}}{\stackrel{\textit{top and bottom}}{2(14.5)(6)}~~ + ~~\stackrel{\textit{left and right}}{2(6)(8.5)}~~ + ~~\stackrel{\textit{front and back}}{2(14.5)(8.5)}}\implies 522.5~ft^2 \\\\\\ ~\hspace{8em}\stackrel{\textit{\LARGE lateral area}}{\stackrel{\textit{left and right}}{2(6)(8.5)}~~ + ~~\stackrel{\textit{front and back}}{2(14.5)(8.5)}}\implies 348.5~ft^2 \\\\[-0.35em] ~\dotfill\\\\ 522.5~~ - ~~348.5\implies \text{\LARGE 174}~ft^2`