I had the random urge to post a note. So here it is.
The area of any regular polygon can be expressed in the form (My proof of this is here)where a is the apothem (or in a circles case its radius) and p is the perimeter.
Because a circle is a polygon with infinitely many sides, this rule applies to circles as well.
The perimeter/circumference of a circle is .
Therefore, the area of a circle can be represented as .
Boom. Done. fin. El fine. Koniec. Ende. The end.
NOW GO SOLVE SOME GREAT PROBLEMS WITH YOUR NEW FOUND KNOWLEDGE!!