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 100f * t ^ 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)
The surface area of a regular triangular pyramid is given by the formula:
A = (1/2) * perimeter of the base * slant height
Since the base of the pyramid is a regular triangle, the perimeter is given by:
3 * length of one side of the base
We are given the base is 6 ft, so the perimeter of the base is:
3 * 6 = 18 ft
We are also given that the slant height is 8 ft.
Plugging these values into the surface area formula, we have:
100f * t^2 = (1/2)(18)(8)
Simplifying further:
100f * t^2 = 72
Dividing both sides by 100:
f * t^2 = 0.72
Since t^2 is positive, we can divide both sides by t^2:
f = 0.72/t^2
To find the height of the base, let's solve for t:
t^2 = 0.72/f
t = sqrt(0.72/f)
Since the height is the slant height minus the height of the base, we have:
height = slant height - t
height = 8 - sqrt(0.72/f)
To the nearest tenth, the height of the base of the outdoor play tent is 8 - sqrt(0.72/f) ft.