The formula for the volume \( V \) of a rectangular pyramid is given by:
\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \]
For a rectangular base, the base area can be calculated using:
\[ \text{base area} = \text{length} \times \text{width} \]
In this case, the dimensions are:
- Height \( h = 75 \) in.
- Width \( w = 111 \) in.
- Length \( l = 111 \) in.
First, let's calculate the base area:
\[ \text{base area} = l \times w = 111 , \text{in.} \times 111 , \text{in.} = 12321 , \text{in.}^2 \]
Now, we can substitute the base area and the height into the volume formula:
\[ V = \frac{1}{3} \times 12321 , \text{in.}^2 \times 75 , \text{in.} \]
Now, calculate the volume:
\[ V = \frac{1}{3} \times 12321 \times 75 = \frac{924075}{3} = 308025 , \text{in.}^3 \]
Thus, the volume of the pyramid-shaped tent is:
\[ \boxed{308,025 , \text{in.}^3} \]