Question

14 pointsMr. Escamilla has a tent that is a triangular prism. The volume of the tentis 280 cubic feet, the width of the base is 8 feet, and the length is 10 feet.What is the height of the tent?8 ft10 ftO oftO 7ft8 ftO oft

Answer 1

We have to put the triangular side as the base.

So, the height of the tent is signified by the red line, h.

Shown below:

The volume of the triangular prism is area of triangle x height

V = A_T x h

Let's find the area of the triangle, A_T:

`\begin{gathered} A_T=(1)/(2)bh \\ A_T=(1)/(2)(8)(h)_{} \\ A_T=4h \end{gathered}`

The height is 10.

The volume is 280.

Substituting into the formula, let's sovle for "h". Shown below:

`\begin{gathered} V=A_T* h \\ 280=4h*10 \\ 40h=280 \\ h=(280)/(40) \\ h=7 \end{gathered}`Answer7 ft