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

6.5 ft.
6.5 ft.

57.3 ft.
57.3 ft.

372 ft.
372 ft.

9.3 ft.

Answer 1

pick one

Answer 2

The formula for the surface area of a regular triangular pyramid is given by:

Surface Area = base area + lateral area

The base area of a regular triangular pyramid is given by:

Base area = (1/2) * base * height

And the lateral area is given by:

Lateral area = (1/2) * perimeter * slant height

Given that the surface area is 100 ft^2, the base is 6 ft, and the slant height is 8 ft, we can set up the equation:

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

Since it is a regular triangular pyramid, the perimeter is equal to 3 times the base. Therefore, we have:

100 = (1/2) * 6 * height + (1/2) * 3 * 6 * 8

100 = 3 * height + 3 * 6 * 8

100 = 3 * height + 144

Subtracting 144 from both sides gives:

-44 = 3 * height

Dividing both sides by 3 gives:

-44/3 = height

Therefore, the height of the base to the nearest tenth is -14.7 ft. However, since the height of a pyramid cannot be negative, we can conclude that the given values for the surface area, base, and slant height do not form a valid triangular pyramid. Therefore, none of the provided options (6.5 ft, 57.3 ft, 372 ft, or 9.3 ft) is correct.

Answer 3

6.5 ft.