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.
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.
The formula for the area (A) of an equilateral triangle with side length (s) is given by:
A = (β3/4) * 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 = (β3/4) * 12^2
Simplifying further:
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 144
A = (β3/4) * 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 = (β3/4) * 144 * 6
Simplifying further:
V = (β3/4) * 864
V β 748.33 cubic feet
Therefore, the volume of the prism is approximately 748.33 cubic feet.