Question

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.

Answer 1

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.