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.

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) * base * slant height + base * height

Plugging in the given values:

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

Simplify:

100 = 3 * 8 + 6 * height
100 = 24 + 6 * height

Subtract 24 from both sides:

76 = 6 * height

Divide both sides by 6:

12.67 = height

Rounded to the nearest tenth, the height of the base is 12.7 ft. Therefore, the correct answer is 6.5 ft.