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You neglected to say whether the 4mm is the radius of the circle, or the diameter,or the circumference. Each possibility gives you a different area.
get off of me i'm a circle not a circle with a line through it
Zero in the normal course of events. You could say you can approximate a circle by an infinite-sided polygon, and then you would have infinite sides and corners. Or you could say a circle has an inside and an outside.
un cercle (masc.)
The is not stated that the circle inside the square was the greatest possible circle, so all one can say is 8pi at most.