The area of a disc (the region inside a circle), often incorrectly called the area of a circle, is $$ \pi r^2 $$ when the circle has radius **r**. Here the symbol $$ \pi $$ (Greek letter pi) denotes, as usual, the constant ratio of the circumference of a circle to its diameter. It is easy to deduce the area of a disk from basic principles: the area of a regular polygon is half its apothem times its perimeter, and a regular polygon becomes a circle as the number of sides increase, so the area of a disc is half its radius times its circumference (i.e. $${1 \over 2} r * 2 \pi r $$ ).

More information can be found here: **en.wikipedia.org/wiki/Area ofa_circle**