To calculate the amount of fabric needed to make the teepee dog bed, we need to find the total surface area of the triangular pyramid, which consists of three triangular faces and one triangular base.
Step 1: Calculate the area of one triangular face.
The area \( A \) of a triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case, the base of the triangular face is 30 inches and the height is 25 inches.
\[ A = \frac{1}{2} \times 30 , \text{inches} \times 25 , \text{inches} = \frac{1}{2} \times 750 , \text{inches}^2 = 375 , \text{inches}^2 \]
Step 2: Calculate the area of all three triangular faces.
Since there are three identical triangular faces, we multiply the area of one face by 3:
\[ \text{Total area of triangular faces} = 3 \times 375 , \text{inches}^2 = 1125 , \text{inches}^2 \]
Step 3: Calculate the area of the base triangular face.
The area of the base is the same as that of the triangular faces:
\[ \text{Area of the base} = 375 , \text{inches}^2 \]
Step 4: Calculate the total surface area.
Now, we add the area of the three triangular faces and the area of the base:
\[ \text{Total surface area} = \text{Total area of triangular faces} + \text{Area of the base} = 1125 , \text{inches}^2 + 375 , \text{inches}^2 = 1500 , \text{inches}^2 \]
Thus, the total amount of fabric needed to cover the teepee dog bed is:
\[ \boxed{1500} , \text{inches}^2 \]
Therefore, the correct answer is 1,500 in.².