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
405 in.2
405 in. squared
292.5 in.2
292.5 in. squared
351 in.2
351 in. squared
502.5 in.2
502.5 in. squared
To find the total fabric needed to make the sign, we need to find the area of each of the three triangular faces.
The area of an equilateral triangle can be found using the formula: A = (sqrt(3)/4) * s^2, where s is the side length of the triangle.
For the three triangular faces with height 18 inches, the area of each face would be:
A = (sqrt(3)/4) * 15 * 18 = 195√3 in.²
Since there are three faces, the total fabric needed would be:
Total fabric = 3 * 195√3 = 585√3 in.²
To find the approximate value, we use the fact that √3 is approximately 1.732:
Total fabric ≈ 585 * 1.732 ≈ 1012.82 in.²
Therefore, the correct answer would be closest to 502.5 in.².
So, the correct answer is:
502.5 in.²
502.5 in. squared