Question

Once the tent is set up how many cubic feet will there be inside?

Answer 1

Let's start by defining that the area of a triangle is calculated using the equation

`A=(1)/(2)b* h`

In the given figure, we have a triangular prism with its face as an isosceles triangle. If we look at the front view of the triangular prism, we have the following dimensions

Whereas it is composed of two right triangles. Hence, the area of the face of the triangular prism is just the area of one of the right triangles multiplied by 2. The length of the base of each right triangle is given but the height is not given. This can be computed using the Pythagorean theorem. The hypotenuse of each right triangle is equal to 26 ft. Hence, to compute for height, we have

`\begin{gathered} h^2=c^2-b^2 \\ h=\sqrt[]{26^2-10^2}=24 \end{gathered}`

The height of both right triangles is 24 ft. Hence, the total area of the face of the triangular prism is

`A=2((1)/(2)b* h)=10ft*24ft=240ft^2`

Finally, to compute the volume of the triangular prism, we just multiply the calculated area of the face of the triangular prism by the length of the triangular prism, which is equal to 40 ft. The volume of the triangular prism is

`V=(240ft^2)(40ft)=9600ft^3`