Question 745052
I hope you know what is the apothem of a regular polygon. If not just google it.

Ok, let us inscribed a circle in a regular polygon so that its radius is equal to the apothem.

The formula of Regular polygon Circumscribing a circle are:
{{{Perimeter = 2nr tan(180/n)}}} and {{{Area = nr^2tan(180/n)}}}

In the perimeter formula, see that {{{tan(180/n)= Perimeter/2nr}}}, substitute it to the Area:
{{{Area = nr^2(P/2nr) = r(48/2)}}} where r = 6
Therefore, Area = 144 sq. unit.