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)
372 ft
6.5 ft
9.3 ft
57.3
The surface area of a regular triangular pyramid is given by the formula:
SA = (1/2) * (base perimeter) * (slant height)
In this case, we know that the surface area is 100 ft², the base is 6 ft, and the slant height is 8 ft. We can use these values to find the height.
The base perimeter of a regular triangular pyramid is equal to 3 times the length of one side of the base. Since the base is a triangle, we can find the length of one side by dividing the base perimeter by 3:
Side length = base / 3 = 6 ft / 3 = 2 ft
Now, we can substitute the values into the surface area formula:
100 ft² = (1/2) * (3 * 2 ft) * (8 ft)
100 ft² = 6 ft * 8 ft
100 ft² = 48 ft
To find the height, we need to divide the surface area by the base perimeter:
Height = Surface area / Base perimeter = 100 ft² / 48 ft
Height ≈ 2.083 ft
Therefore, the height of the base to the nearest tenth is approximately 2.1 ft.