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?
351 in.2
405 in.2
292.5 in 2
502.5 in 2
To calculate the total amount of fabric needed to make the sign, we first need to find the area of each of the three triangular faces.
The area of a triangle is calculated using the formula A = 1/2 * base * height. For the triangles with the base length of 15 inches and height of 18 inches, the area is:
A = 1/2 * 15 * 18 = 135 square inches
Since there are three identical faces, the total area of fabric for these faces is 3 * 135 = 405 square inches.
Therefore, the total amount of fabric needed to make the sign is 405 square inches.
So the correct answer is 405 in.2.