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)Responses1,365 in.21,365 in. squared1,450 in.21,450 in. squared1,495 in.21,495 in. squared1,515 in.2
1,365 in. squared
To find the total surface area of the teepee, we first calculate the area of the equilateral triangle by using the formula: A = (sqrt(3)/4) * side^2.
A = (sqrt(3)/4) * 30^2
A = (1.732/4) * 900
A = 0.433 * 900
A = 390 in. squared
Since there are two equilateral triangles on the teepee, the total area for those two faces is: 390 in. squared * 2 = 780 in. squared
Next, we calculate the area of the three rectangular faces that make up the teepee. The area of each rectangle is given by: A = base * height.
For the rectangular faces, we have:
2 * (26 in. * 25 in.) = 1,300 in. squared
Summing up all the areas, we get:
780 in. squared (equilateral triangles) + 1,300 in. squared (rectangular faces) = 2,080 in. squared
Therefore, the amount of fabric needed to make the teepee dog bed is 2,080 in. squared.