AThe area of an equilateral triangle is given by the formula:
A = (sqrt(3)/4) * s^2
where A is the area and s is the length of one side.
If the original length of the side is x, then the new length is 6x. Therefore, we can write:
A(6x) = (sqrt(3)/4) * (6x)^2
Simplifying:
A(6x) = (sqrt(3)/4) * 36 * x^2
A(6x) = 9 * sqrt(3) * x^2
Therefore, the function representing the area of an equilateral triangle with sides of length six times the original length is:
A(6x) = 9 * sqrt(3) * x^2: