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.
57.3 ft.
57.3 ft.
9.3 ft.
To find the height of the base, we can use the formula for the surface area of a triangular pyramid:
Surface Area = (1/2) x (base perimeter) x (slant height) + (base area)
We are given that the surface area is 100 ft^2, the base is 6 ft, and the slant height is 8 ft.
So, we have:
100 = (1/2) x (6+6+6) x 8 + 1/2 x (6 x 6)
Simplifying,
100 = (1/2) x 18 x 8 + 1/2 x 36
100 = 72 + 18
100 = 90
This equation is not true, so the given values are not correct.