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 in 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.
A. 292. 5 in.²
B. 502.5 in.²
C. 405 in.²
D. 351 in.²
To find the total surface area of the triangular pyramid, we first need to calculate the area of the three triangular faces.
The area of a triangle can be calculated using the formula: Area = 0.5 * base * height
For the equilateral triangle faces:
Area = 0.5 * 15 in. * 18 in. = 135 in.²
Since there are three identical faces, the total area of these three faces is:
3 * 135 in.² = 405 in.²
Now we need to calculate the area of the base triangle, which is an equilateral triangle with side lengths of 15 inches. The formula to calculate the area of an equilateral triangle is:
Area = (√3 / 4) * side²
Area = (√3 / 4) * 15 in. * 15 in. = 97.43 in.²
So, the total surface area of the triangular pyramid is:
405 in.² + 97.43 in.² = 502.43 in.²
Therefore, the amount of fabric needed to make the sign is approximately 502.5 in.², which is option B.