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.
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.
1 answer