Niko has an outdoor play tent in the form of a regular triangular pyramid, covered in fabric on all four sides. The surface area of the tent is 100 ft.2 , the base is 6 ft., and the slant height is 8 ft. What is the height of the base to the nearest tenth
The surface area of a regular triangular pyramid is given by the formula S = 1/2 * P * l, where P is the perimeter of the base and l is the slant height.
The perimeter of the base is equal to three times the length of one side of the base, since it is a regular triangle. We are given that the base is 6 ft, so the perimeter of the base is 3 * 6 = 18 ft.
Plugging in the given values, we have:
100 = 1/2 * 18 * 8
100 = 9 * 8
100 = 72
This equation is not true, so there must be an error in the problem statement or in our calculations.