Question 623197
The area of a regular polygon is given by:
{{{A = (1/2)*P*a}}} where P = perimeter and a = the length of the apothem.
Note: The apothem is the distance from the center to the midpoint of a side.
In this problem, we'll find the perimeter then divide it by 6 (a regular hexagon has 6 equal sides.)
{{{A = (1/2)*P*a}}} Substitute {{{A = x^3}}} and {{{a = x}}}
{{{x^3 = (1/2)*P*x}}} Divide both sides by x.
{{{x^2 = (1/2)*P}}} Multiply both sides by 2.
{{{2x^2 = P}}}
Now that we have the perimeter, P, we can divide by 6 to find the length of one side, S.
{{{S = P/6}}}
{{{S = 2x^2/6}}} Simplify.
{{{S = x^2/3}}} or {{{S = (1/3)x^2}}}