A “wet floor” warning sign is in the shape of a triangular pyramid without a base. The edge length of the base equilateral triangle is 15 inches, the height of the base triangle is 13 inches, and the height of the triangular faces is 18 inches. How much fabric is needed to make the sign given the base does not need fabric?(1 point)
Responses
351 in.2
351 in. squared
405 in.2
405 in. squared
502.5 in.2
502.5 in. squared
292.5 in.2
The total surface area of a triangular pyramid can be calculated using the formula:
Surface Area = (1/2) * base perimeter * slant height + base area
First, calculate the base perimeter:
Perimeter of equilateral triangle = 3 * side length
Perimeter = 3 * 15 inches = 45 inches
Now, calculate the slant height:
Slant height for an equilateral triangle = square root of ((side length)^2 - (height)^2)
Slant height = √(15^2 - 13^2) = √(225 - 169) = √56 ≈ 7.48 inches
Now, calculate the base area:
Area of equilateral triangle = (sqrt(3) / 4) * (side length)^2
Base area = (sqrt(3) / 4) * (15^2) ≈ 97.43 square inches
Now, calculate the total surface area:
Surface Area = (1/2) * 45 * 7.48 + 97.43
Surface Area = 335.1 + 97.43
Surface Area ≈ 432.53 square inches
Therefore, the amount of fabric needed to make the sign is approximately 432.53 square inches, which is closest to 405 in. squared.