The surface area of a triangular pyramid can be calculated using the formula:
Surface Area = Base Area + 1/2 * Perimeter of Base * Slant Height
First, we calculate the base area of the equilateral triangle base:
Base Area = (sqrt(3) / 4) * side^2
Base Area = (sqrt(3) / 4) * 15^2
Base Area = (sqrt(3) / 4) * 225
Base Area = 97.43 cm²
Now, we calculate the perimeter of the base:
Perimeter of Base = 3 * side
Perimeter of Base = 3 * 15
Perimeter of Base = 45 cm
Now, we can substitute these values into the surface area formula:
Surface Area = 97.43 + 1/2 * 45 * 17
Surface Area = 97.43 + 382.5
Surface Area = 479.93 cm²
Therefore, the surface area of the triangular pyramid is approximately 480 cm².