Question

Find the volume of the 3-D solid shown below:

Answer 1

Check the picture below.

so is really just a thick trapezoid, or namely a trapezoidal prism 5 inches thick.

so if we just get the area of the trapezoidal face and multiply by the thickness, we'd get it's volume

$\bf \textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} a,b=\stackrel{parallel~sides}{bases}\\ h=height\\[-0.5em] \hrulefill\\ a = 8\\ b = 13\\ h = 6 \end{cases}\implies A=\cfrac{6(8+13)}{2}\implies A=63 \\\\\\ \stackrel{\textit{area of the trapezoidal prism}}{63\cdot 5\implies \stackrel{in^3}{315}}$