The shape of this jigsaw puzzle piece may be viewed as a square of side \(s\) to which four circles of radius \(r\) have been added. The square and the circles overlap. Assume that the part of the circle circumference that sticks out forms an \(240^\circ\) arc.

The total area of the puzzle piece may be written as \[A = s^2 + c\cdot r^2.\] Calculate the value of \(c\).

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