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.

372 ft.
372 ft.

9.3 ft.
9.3 ft.

57.3 ft.

Answer 1

Each lateral face area = 1/2 * base * slant height = 1/2 * 6 * 8 = 24.
Three lateral faces area = 3 * 24 = 72.
Base area = total surface area − lateral area = 100 − 72 = 28.
Height of the base (triangle) = 2 * (base area) / (base) = 2*28 / 6 = 56/6 ≈ 9.333... ≈ 9.3 ft.

Answer: 9.3 ft.