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
292.5 in.2
292.5 in. squared
502.5 in.2
502.5 in. squared
To find the total surface area of the triangular pyramid, we need to calculate the area of the three triangular faces.
The area of an equilateral triangle can be calculated using the following formula:
Area = (√3 / 4) * (side length)^2
1. Area of base triangle:
Area_base = (√3 / 4) * 15^2
Area_base = (√3 / 4) * 225
Area_base = (1.732 / 4) * 225
Area_base = 1.732 * 56.25
Area_base = 97.4325 in^2
2. Area of one triangular face:
Area_face = (1/2) * base * height
Area_face = (1/2) * 15 * 18
Area_face = 135 in^2
3. Total fabric needed:
Total_area = 3 * Area_face
Total_area = 3 * 135
Total_area = 405 in^2
Therefore, the correct answer is:
405 in^2