The surface area of a regular triangular pyramid can be found by the formula:
SA = (1/2)(p)(s) + (b)(h)
where SA is the surface area, p is the perimeter of the base, s is the slant height, b is the base area, and h is the height of the pyramid.
In this case, we are given that the surface area is 100 ft^2, the base is 6 ft, and the slant height is 8 ft.
We can substitute the given values into the formula:
100 = (1/2)(6)(8) + (6)(h)
Simplifying the equation:
100 = 24 + 6h
Subtracting 24 from both sides:
76 = 6h
Dividing both sides by 6:
h = 12.67 ft
Rounding to the nearest tenth:
h = 12.7 ft
The height of the base of the tent is approximately 12.7 ft.
Therefore, the answer is option D. 9.3 ft (which is incorrect).
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?
A.6.5 ft.
B.57.3 ft.
C.372 ft.
D.9.3 ft.
1 answer