Question

a parking garage has a tented area with a slanted roof.
dimensions of the triangular prism

• base - 20 feet by 20 feet
• height - 40 feet

dimensions of the rectangular prism

• base - 15 feet by 40 feet
• height - 20 feet

what is the total amount of volume inside the parking garage?
ft³

Explanation:

Step1: Calculate the volume of the rectangular prism

The formula for the volume of a rectangular prism is \(V = l\times w\times h\). Here, \(l = 40\) ft, \(w=15\) ft, \(h = 20\) ft.

$$V_{rectangular}=40\times15\times20=12000\ \text{ft}^3$$

Step2: Calculate the volume of the triangular prism

The formula for the volume of a triangular prism is \(V=\frac{1}{2}\times b\times h\times l\). The base of the triangle \(b = 20\) ft, the height of the triangle \(h = 20\) ft, and the length \(l=40\) ft.

$$V_{triangular}=\frac{1}{2}\times20\times20\times40 = 8000\ \text{ft}^3$$

Step3: Calculate the total volume

Add the volumes of the two prisms together.

$$V_{total}=V_{rectangular}+V_{triangular}=12000 + 8000=20000\ \text{ft}^3$$

Answer:

\(20000\)