A prism has an equilateral triangle for its base. One side of the base measures 12 ft and the altitude of the prism is 6 ft. Find the volume.
To find the volume of a prism, we need two measurements: the area of the base and the height of the prism. In this case, since the base is an equilateral triangle, we can use the formula for the area of an equilateral triangle.
The formula for the area (A) of an equilateral triangle with side length (s) is given by:
A = (√3/4) * s^2
In this problem, we are given that one side of the base measures 12 ft. Therefore, substituting this value into the formula, we get:
A = (√3/4) * 12^2
Simplifying further:
A = (√3/4) * 144
A = (√3/4) * 144
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A = (√3/4) * 144
Once we have the area of the base, we can find the volume (V) of the prism by multiplying the base area by the height of the prism (h):
V = A * h
In this problem, the height of the prism is given to be 6 ft. Therefore, substituting the base area and height into the formula, we get:
V = (√3/4) * 144 * 6
Simplifying further:
V = (√3/4) * 864
V ≈ 748.33 cubic feet
Therefore, the volume of the prism is approximately 748.33 cubic feet.
V = 1/3 area of base * alt
area of triangular base = 1/2 s * h
Since it is equilateral, use Pythagorean theorem to find h.
h^2 + (1/2s)^2 = s^2
I'll let you do the calculations.