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.
6.5 ft.
6.5 ft.
9.3 ft.
9.3 ft.
57.3 ft.
To find the height of the base, we can use the formula for the surface area of a regular triangular pyramid:
Surface area = (base area) + (lateral area)
The base area of a triangular pyramid is given by:
Base area = (1/2) * base * height
And the lateral area is given by:
Lateral area = (perimeter of base) * slant height / 2
Given that the base is 6 ft and the slant height is 8 ft, we can start substituting the values into the formulas. Let's use h to represent the height of the base:
Surface area = (1/2) * 6 * h + (6 + 6 + 6) * 8 / 2
100 = 3h + 36
Subtracting 36 from both sides:
64 = 3h
Dividing both sides by 3:
h = 64/3 ≈ 21.3 ft
Therefore, the height of the base to the nearest tenth is 21.3 ft.