The formula for circumference of a circle with radius #r# is #2 pi r#.

The formula for the area of a circle with radius #r# is #pi r^2#.

#pi ~~ 3.14#

So the radius of our circle is #6.28 / (2 pi) ~~ 6.28 / (2 * 3.14) = 1#

and its area is #pi r^2 ~~ 3.14 * 1^2 = 3.14#

The number #pi# is defined as the ratio of the circumference of a circle to its diameter (i.e. to twice its radius), hence the formula #2 pi r#.

To see that the area of a circle is #pi r^2# you can divide it into a number of equal segments and stack them head to tail to form a sort of parallelogram with 'bumpy' sides. the long sides will be about half the circumference in length - that is #pi r#, while the height of the parallelogram will be about #r#. So the area is seen to be about #pi r^2#.

This approximation gets better the more segments you have, but here's an animated illustration I put together...