Question

What is the volume of this prism?

Answer 1

Check the picture below.

btw that picture above is misleading, whenever is 3 longer than 7? and 2 longer than 7? =)

so let's just get the area of the trapezoidal face and multiply that by the depth of 7.

`\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=2\\ b=4\\ h=3 \end{cases}\implies A=\cfrac{3(2+4)}{2}\implies A=9 \\\\[-0.35em] ~\dotfill\\\\ (9)(7)\implies \text{\LARGE 56}\qquad \impliedby volume`