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
292.5 in.2
292.5 in. squared
502.5 in.2
502.5 in. squared
351 in.2
351 in. squared
405 in.2
The total surface area of a triangular pyramid can be calculated using the formula:
Surface Area = 0.5 * base perimeter * slant height + base area
First, calculate the base perimeter:
base perimeter = 3 * edge length = 3 * 15 = 45 inches
Next, calculate the slant height of the triangular faces:
slant height = sqrt((height of triangular faces)^2 + (0.5 * edge length)^2) = sqrt(18^2 + 7.5^2) = sqrt(324 + 56.25) = sqrt(380.25) = 19.5 inches
Now, calculate the base area:
base area = 0.5 * edge length * height of base triangle = 0.5 * 15 * 13 = 97.5 square inches
Finally, plug the values into the formula to find the total surface area:
Surface Area = 0.5 * 45 * 19.5 + 97.5 = 22.5 * 19.5 + 97.5 = 438.75 + 97.5 = 536.25 square inches
Therefore, the answer is 536.25 square inches, which is not listed as an option. However, the closest option is 502.5 in.2.