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. 9.3 ft. 9.3 ft. 57.3 ft. 57.3 ft. 6.5 ft.

Question

FInd the closest one to the actual answer!!

Answer 1

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

Surface Area = (base perimeter * slant height) / 2

We know that the surface area is 100 ft^2, the base is 6 ft, and the slant height is 8 ft. Plugging these values into the formula, we get:

100 = (6 * slant height) / 2

Simplifying:

200 = 6 * slant height

Dividing by 6:

33.3 = slant height

Now, to find the height, we can use the Pythagorean theorem:

Height^2 = slant height^2 - (base/2)^2

Height^2 = 33.3^2 - (6/2)^2
Height^2 = 1110.89 - 9
Height^2 ≈ 1101.89

Now, we can take the square root to find the height:

Height ≈ √1101.89
Height ≈ 33.2

Rounded to the nearest tenth, the height of the base is approximately 33.2 ft. Hence, 9.3 ft is the closest option provided.