A teepee dog bed is in the shape of a triangular pyramid. How much fabric is needed to make the teepee given the following dimensions? The slant height of the equilateral triangular faces is 25 in. The height of the base triangle is 26 in. The base of the equilateral triangles is 30 in. (1 point)
To find the total fabric needed to make the teepee, we first need to calculate the area of all the triangular faces.
The area of an equilateral triangle is given by the formula:
A = (√3/4) * s^2
where A is the area and s is the side length of the triangle.
For the base triangle:
A = (√3/4) * 30^2
A = (√3/4) * 900
A = (√3/4) * 900
A = 15√3
Now, we need to find the area of the triangular faces. The slant height is used as the height of the triangle:
A = (√3/4) * 25^2
A = (√3/4) * 625
A = (√3/4) * 625
A = 2688.675
Since there are 3 equilateral triangular faces, we need to multiply the area by 3:
Total fabric needed = 15√3 + 3 * 2688.675
Total fabric needed = 15√3 + 8066.025
Total fabric needed ≈ 8081.025 in^2
Therefore, approximately 8081.025 square inches of fabric are needed to make the teepee dog bed.