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 ft², the base is 6 ft, and the slant height is 8 ft. What is the height of the base to the nearest tenth?

A. 6.5 ft
B. 9.3 ft
C. 372 ft
D. 57.3 ft

Answer 1

Lateral area = 3 × (1/2)(base)(slant height) = 3 × (1/2)(6)(8) = 72 ft².
So base area = total surface − lateral = 100 − 72 = 28 ft².
If the base side is 6, its area = (1/2)(6)(base height) = 3 × (base height) = 28, so base height = 28/3 ≈ 9.3 ft.

Answer: B.