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.?
, 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)
The surface area of a regular triangular pyramid can be calculated using the formula: Surface Area = (1/2) * perimeter of base * slant height.
The base of the pyramid is a regular triangle, so its perimeter can be calculated by multiplying the length of one side by 3: 6 ft * 3 = 18 ft.
Plugging the values into the formula: 100 ft² = (1/2) * 18 ft * 8 ft.
Now, let's solve the equation:
100 ft² = 9 ft * 8 ft
Divide both sides of the equation by 9 ft:
100 ft² / 9 ft = 8 ft
11.1 ft ≈ height of the base to the nearest tenth. Answer: \boxed{11.1}.