To find the height of the base, we first need to calculate the area of one triangular face of the pyramid.
The formula for the surface area of a pyramid is:
Surface Area = Base Area + (0.5 * Perimeter of Base * Slant Height)
Since the base is a triangle, the formula for the area of a triangle is:
Area = (base * height) / 2
Given that the surface area of the tent is 100 ft², the base is 6 ft, and the slant height is 8 ft, we can substitute these values into the formula:
100 = (6 * h) / 2 + (0.5 * 6 * 8)
Simplify this equation:
100 = 3h + 24
Subtract 24 from both sides:
76 = 3h
Divide by 3:
h = 76 / 3
h = 25.3 ft
Therefore, the height of the base is approximately 25.3 feet.