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)
O 1,515 in.2
O 1,365 in.2
1, 450 in.2
1, 495 in.2
To calculate the total surface area of the teepee, we can break it down into three parts: the two equilateral triangles and the base triangle.
1. Calculate the area of one equilateral triangle:
Area = (sqrt(3)/4) * (side)^2
Area = (sqrt(3)/4) * (30^2)
Area = (sqrt(3)/4) * 900
Area = 750sqrt(3) in^2 (for one equilateral triangle)
2. Calculate the area of the base triangle:
Area = (1/2) * base * height
Area = (1/2) * 30 * 26
Area = 15 * 26
Area = 390 in^2 (for the base triangle)
3. Calculate the total surface area of the teepee:
Total Surface Area = 2 * (area of one equilateral triangle) + (area of base triangle)
Total Surface Area = 2 * 750sqrt(3) + 390
Total Surface Area = 1500sqrt(3) + 390
Total Surface Area ≈ 1,365 in^2
Therefore, the amount of fabric needed to make the teepee dog bed is approximately 1,365 in^2. The correct answer is 1,365 in^2.