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.

9.3 ft.
9.3 ft.

57.3 ft.
57.3 ft.

6.5 ft.
6.5 ft.

Answer 1

Use SA = base area + 3(lateral face areas).
Base area = (√3/4)·6^2 = 9√3. Each lateral face area = 1/2·6·(slant height) = 3·l, so three faces = 9l.

100 = 9√3 + 9l
9l = 100 − 9√3
l = (100 − 9√3)/9 ≈ 9.38

To the nearest tenth (closest choice given): 9.3 ft.