Question

Help please!!


I can’t figure this out

Answer 1

Check the picture below.

so the prism is a "right square" prism, namely it has only right-angles and two of its faces are a square, namely the front and back. We know it has a surface are of 220 cm², so let's check what the width "w" is first.

`\stackrel{\textit{\huge surface area}}{\stackrel{\textit{front and back}}{2(5)(5)}~~ + ~~\stackrel{\textit{left and right}}{2(5)(w)}~~ + ~~\stackrel{\textit{top and bottom}}{2(5)(w)}}~~ = ~~\stackrel{cm^2}{\textit{\Large 220}} \\\\\\ 50~~ + ~~10w~~ + ~~10w~~ = ~~220\implies 50+20w=220\implies 20w=170 \\\\\\ w=\cfrac{170}{20}\implies w=\cfrac{17}{2} \\\\[-0.35em] ~\dotfill`

`\stackrel{\textit{\huge volume}}{\stackrel{length}{(5)}~~\stackrel{height}{(5)}~~\stackrel{width}{\left( \cfrac{17}{2}\right)}}\implies \cfrac{425}{2}\implies 212.5`