To calculate the total amount of fabric needed to make the teepee dog bed in the shape of a triangular pyramid, we need to find the area of the triangular faces and the base.
Step 1: Calculate the area of one triangular face.
The area \( A \) of a triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
Given:
- Base of the triangle \( = 30 \) inches
- Height of the triangle \( = 25 \) inches
Substituting the values into the formula:
\[ A = \frac{1}{2} \times 30 \times 25 = \frac{1}{2} \times 750 = 375 \text{ in}^2 \]
Step 2: Calculate the area of the base.
Since the base is also a triangle with the same dimensions: \[ \text{Area of the base} = 375 \text{ in}^2 \]
Step 3: Calculate the total area of the teepee.
There are 3 triangular faces and 1 base:
\[ \text{Total Area} = 3 \times \text{area of one triangular face} + \text{area of the base} \]
Substituting the calculated areas:
\[ \text{Total Area} = 3 \times 375 + 375 = 1125 + 375 = 1500 \text{ in}^2 \]
Conclusion
The total amount of fabric needed to make the teepee is:
\[ \boxed{1500 \text{ in}^2} \]
So the correct answer is 1,500 in.².