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)
The total surface area of the triangular pyramid can be calculated as follows:
1. Calculate the area of the equilateral triangle base:
Area_base = (sqrt(3)/4)*(edge length)^2
Area_base = (sqrt(3)/4)*(15)^2
Area_base = (sqrt(3)/4)*225
Area_base ≈ 97.43 square inches
2. Calculate the area of the three triangular faces:
Area_faces = (1/2)*base*height
Area_faces = (1/2)*15*18
Area_faces = 135 square inches
3. Calculate the total surface area of the triangular pyramid:
Total_area = Area_base + Area_faces
Total_area = 97.43 + 135
Total_area ≈ 232.43 square inches
Since the base does not need fabric, the total area of fabric needed to make the sign is approximately 232.43 square inches.