Nicko 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 squared., the base is 6 ft., and the slant height is 8 ft. What is the height of the base to the nearest tenth
6.5 ft
372 ft
57.3 ft
9.3 ft
The surface area of a regular triangular pyramid is given by the formula:
SA = (s^2 * √3) / 4 + b * l
Where SA is the surface area, s is the slant height, b is the base, and l is the slant height.
Plugging in the given values:
100 = (8^2 * √3) / 4 + 6 * 8
Simplifying the equation:
100 = (64 * √3) / 4 + 48
100 = (16 * √3) + 48
52 = 16 * √3
√3 = 52 / 16
√3 ≈ 3.25 (rounded to the nearest hundredth)
Since the height of the base is the same as the slant height, the height is approximately 3.25 feet.
Therefore, the closest option is 9.3 ft.