To find the height of the base, we can use the formula for the surface area of a regular triangular pyramid, which is given by the formula:
Surface Area = (1/2) * base * slant height + (1/2) * (base * height of triangle on base)
In this case, we are given the surface area as 100 ft^2, the base as 6 ft, and the slant height as 8 ft. We can substitute these values into the formula and solve for the height of the triangle on the base.
100 = (1/2) * 6 * 8 + (1/2) * (6 * h)
Simplifying this equation, we get:
100 = 24 + 3h
Subtracting 24 from both sides:
76 = 3h
Dividing both sides by 3:
h = 76/3 ≈ 25.3 ft
Therefore, the height of the base is approximately 25.3 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
6.5 ft.
6.5 ft.
57.3 ft.
57.3 ft.
9.3 ft.
9.3 ft.
372 ft.
1 answer