A building contractor needs to compute the volume of air contained in a building with a rectangular floor, as shown in the figure below. The building is 20 feet long, 4 yards wide, 9
1
2
feet high on two sides 9 and a half feet high on two sides and 15 feet high from the floor to the peak. What is the volume of air in the building in cubic feet?

The volume of air in the building is

Step-by-step explanation:

The attached image shows the shape of the building and the described dimensions.

As we can see, the building is a combanation of a triangular prism and a parallelepiped. So, we have to calculate the volume in both figures and sum the total to obtain the whole volume.

The volume of a Triangular prism is the area of the triangle multiplied by the height of the prism:

(1)

Where:

is the base of thee triangle

is the height of thee triangle

is the height of triangular prism

Then:

(2)

(3)

The volume of a parallelepiped is the area of the rectangle multiplied by the height:

(4)

Where:

is the length

is the width

is the height

(5)

(6)

Now, the total volume is:

(7)

This is the volume of air in the building