To find the surface area of the triangular pyramid, we need to find the area of the base and the area of the three triangular faces.
The area of an equilateral triangle base can be calculated using the formula Area = (sqrt(3)/4) * s^2, where s is the side length of the equilateral triangle. In this case, s = 14, so the area of the base is (sqrt(3)/4) * 14^2 = 84 in^2.
The area of each triangular face can be calculated by using the formula Area = 0.5 * base * height. The height of each triangular face is the slant height, which is 13 inches, and the base of each triangular face is the side length of the base, 14 inches.
So the area of each triangular face is 0.5 * 14 * 13 = 91 in^2.
Since there are three triangular faces, the total area of the three faces is 3 * 91 = 273 in^2.
Therefore, the total surface area of the triangular pyramid is the sum of the base area and the three triangular faces, which is 84 + 273 = 357 in^2.
Therefore, the correct answer is:
357 in.2
357 in. squared