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
502.5 in.2
502.5 in. squared
405 in.2
405 in. squared
292.5 in.2
292.5 in. squared
351 in.2
wrong
The formula to calculate the surface area of a triangular pyramid is:
Surface Area = Base Area + (1/2 x Perimeter of Base x Slant Height)
Base Area = 15 in x 13 in = 195 in^2 (since the base does not need fabric, we don't include it in the final answer)
Perimeter of Base = 3 x 15 in = 45 in
Slant Height = 18 in
Plugging these values into the formula:
Surface Area = 0 + (1/2 x 45 in x 18 in) = (1/2 x 45 in x 18 in) = 405 in^2
Therefore, the correct answer is:
405 in.2