The surface area of a triangular pyramid can be calculated using the formula:
Surface Area = (1/2) * base * slant height + (1/2) * (perimeter of base) * height
Given that the surface area is 100 ft^2, the base is 6 ft, the slant height is 8 ft, and we need to find the height of the base.
Substitute the given values into the formula to get:
100 = (1/2) * 6 * 8 + (1/2) * (6 + 6 + 6) * h
100 = 24 + 9h
9h = 76
h = 76 / 9
h ≈ 8.44 ft
Therefore, the height of the base to the nearest tenth is approximately 8.4 ft.
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?(1 point) Responses 372 ft. 372 ft. 57.3 ft. 57.3 ft. 9.3 ft. 9.3 ft. 6.5 ft.
1 answer