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)
O 372 ft.
6.5 ft
9.3 ft.
57.3 ft.
To find the height of the triangular pyramid, we need to use the formula for the surface area of a regular triangular pyramid:
Surface Area = (1/2) * base * slant height
We are given the surface area as 100 ft^2, the base as 6 ft, and the slant height as 8 ft. Plugging these values into the formula, we get:
100 = (1/2) * 6 * 8
100 = 24
The equation is not true, so we made an error in our calculations. Let's try again.
The formula for the surface area of a regular triangular pyramid is:
Surface Area = (1/2) * base * slant height + base^2 / 4
Plugging in the given values, we get:
100 = (1/2) * 6 * 8 + 6^2 / 4
100 = 24 + 36 / 4
100 = 24 + 9
This equation is also not true, so we made another error in our calculations. Let's try again by using the correct formula:
Surface Area = (1/2) * base * slant height + base^2 / 2
Plugging in the given values, we get:
100 = (1/2) * 6 * 8 + 6^2 / 2
100 = 24 + 36 / 2
100 = 24 + 18
100 = 42
Once again, this equation is not true, so we made another error in our calculations. Let's try using a different approach to solve for the height of the pyramid.
The surface area of a regular triangular pyramid can also be calculated using the formula:
Surface Area = base * height / 2
We are given the surface area as 100 ft^2 and the base as 6 ft. Plugging these values into the formula, we can solve for the height:
100 = 6 * height / 2
100 = 3 * height
height = 100 / 3
To find the height to the nearest tenth, we can round the result:
height ≈ 33.33 ft
So, the height of the base to the nearest tenth is 33.3 ft. None of the given answer choices are correct.