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
To find the surface area of the triangular pyramid, we need to find the area of two triangular faces (the lateral faces) and one triangular face (the base does not need fabric).
First, let's calculate the area of the lateral faces:
Area of one lateral face = 0.5 * base * height
Area of one lateral face = 0.5 * 15 * 18
Area of one lateral face = 135 square inches
Since there are two lateral faces, the total area of the lateral faces = 135 * 2 = 270 square inches
Now, let's calculate the area of the triangular base:
Area of the base = 0.5 * base * height
Area of the base = 0.5 * 15 * 13
Area of the base = 97.5 square inches
The total fabric needed to make the sign is the sum of the lateral faces and the base area:
Total fabric needed = 270 + 97.5
Total fabric needed = 367.5 square inches
Therefore, the answer is closest to 292.5 in.².