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) Responses 1,515 in.2 1,515 in. squared 1,495 in.2 1,495 in. squared 1,450 in.2 1,450 in. squared 1,365 in.2
To find the total amount of fabric needed to make the teepee, we need to calculate the surface area of all four triangular faces.
The formula to calculate the surface area of a triangular pyramid is:
Surface Area = 1/2 * base perimeter * slant height + base area
First, let's calculate the base perimeter of the equilateral triangle:
Base perimeter = 3 * base length = 3 * 30 in = 90 in
Now, let's calculate the surface area of one triangular face:
Surface Area = 1/2 * 90 in * 25 in + (1/2 * base length * height) = 1125 in + 450 in = 1575 in^2
Since there are four triangular faces on the teepee, the total fabric needed is:
Total Fabric = 4 * 1575 in^2 = 6300 in^2
Therefore, the answer is 1,575 in. squared.