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.

1 answer

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.