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.
A. 1,495 in
B. 1,515 in
C. 1,450 in
D. 1,365 in
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.
First, let's calculate the area of the equilateral triangle base:
Area = (sqrt(3) / 4) * (base length)^2
Area = (sqrt(3) / 4) * (30)^2
Area = (1.732 / 4) * 900
Area = 1.732 * 225
Area = 389.7 in^2
Next, let's calculate the lateral area of the triangular pyramid:
Lateral area = (1/2) * (perimeter of base) * (slant height)
Lateral area = (1/2) * (3 * base) * 25
Lateral area = 1.5 * 90 * 25
Lateral area= 3375 in^2
Now, let's calculate the total surface area of the triangular pyramid:
Total surface area = base area + lateral area
Total surface area = 389.7 + 3375
Total surface area = 3764.7 in^2
Since there are four triangular faces to the teepee, the total fabric needed will be:
4 * 3764.7 = 15058.8 in^2
Therefore, the answer is not provided in the options given.