Answer: The area of the base of the triangular pyramid is given as 15.6 in² and each side of the base is 6 in, so we can use the formula for the area of an equilateral triangle to find the height of the base:
A = (s^2 * sqrt(3)) / 4
where s is the side length of the triangle. Plugging in the values, we get:
15.6 = (6^2 * sqrt(3)) / 4
Solving for the height of the base, h:
h = (4 * 15.6) / (6^2 * sqrt(3)) = 4 / sqrt(3)
Next, we can use the Pythagorean theorem to find the height of the pyramid, since the slant height is given:
h^2 + (base/2)^2 = slant height^2
where base is the length of one side of the base of the pyramid. Plugging in the values, we get:
h^2 + (6/2)^2 = 8^2
Solving for h:
h = sqrt(64 - 9) = sqrt(55)
Finally, the surface area of the pyramid can be found using the formula:
SA = base area + (perimeter * slant height) / 2
where perimeter is the total length of the sides of the base. Plugging in the values, we get:
SA = 15.6 + (3 * 6 * 8) / 2 = 15.6 + 36 = 51.6 in²
So, the surface area of the triangular pyramid is 51.6 in².
Explanation: