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)

Question

Responses

372 ft.
372 ft.

6.5 ft.
6.5 ft.

9.3 ft.
9.3 ft.

57.3 ft.

Answer 1

To find the height of the base of the triangular pyramid, we can use the formula for the surface area of a regular triangular pyramid:

Surface Area = (1/2) * base * slant height + base * height

Since we're given that the surface area is 100 ft², the base is 6 ft, and the slant height is 8 ft, we can plug these values into the formula:

100 = (1/2) * 6 * 8 + 6 * height

Simplifying, we get:

100 = 24 + 6 * height

Subtracting 24 from both sides, we get:

76 = 6 * height

Dividing both sides by 6, we get:

height = 76/6 = 12.7 ft

Therefore, the height of the base is approximately 12.7 ft to the nearest tenth.

Answer 2

pick the correct choice i gave you

Answer 3

The correct choice is:

9.3 ft.

Answer 4

was the answer right