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?(1 point)
Responses
57.3 ft.
57.3 ft.
9.3 ft.
9.3 ft.
6.5 ft.
6.5 ft.
372 ft.
To find the height of the base of the triangular pyramid, we can use the formula for the surface area of a triangular pyramid:
Surface area = (base area) + (lateral area)
The base area of a triangular pyramid is equal to half the base multiplied by the height of the base. We know the base is 6 ft, so we just need to find the height.
100 = (1/2)*6*h + (lateral area)
The lateral area of a triangular pyramid can be found using the formula:
lateral area = (perimeter of base) * (slant height) / 2
We know the slant height is 8 ft, and the base is 6 ft, so the perimeter of the base is 3*6 = 18 ft.
So the lateral area = (18 * 8) / 2 = 72 ft^2.
Substituting the values into the previous equation, we have:
100 = (1/2)*6*h + 72
Simplifying the equation, we get:
100 - 72 = 3h
28 = 3h
h = 28/3 = 9.3 ft (rounded to the nearest tenth).
Therefore, the height of the base of the triangular pyramid is 9.3 ft.