Question

I need help finding the volume of this figure.

Answer 1

Answer:

hello

Step-by-step explanation:

hello

Answer 2

so the figure is really just a right triangular prism below a triangular pyramid.

now, we can say that the triangular face of the prism has a height of 12 and a base of 9, and its volume is simply the area of the triangular face times the length, whilst the volume of the pyramid is just the same as any other pyramid, Base area times height, Check the picture below.

so let's just get their volume and add them up.

$\stackrel{\textit{\large volume of the triangular prism}}{\stackrel{\textit{area of the triangular face}}{\left[ \cfrac{1}{2}(\stackrel{b}{9})(\stackrel{h}{12}) \right]}(\stackrel{length}{10})\implies (54)(10)\implies 540} \\\\[-0.35em] ~\dotfill$

$\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3}~~ \begin{cases} B=base's~area\\ h=height\\[-0.5em] \hrulefill\\ B=54\\ h=14 \end{cases}\implies V=\cfrac{(54)(14)}{3}\implies V=252 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{volumes summed up}}{540~~ + ~~252\implies 792~ft^3}~\hfill$

how do we know the height of the pyramid?

well, from bottom to top the figure is 24 ft high, the prism is 10 ft high, so 24 - 10 = yeap, you guessed it.