Given n circles and a perimeter p, the total area of the convex hull is A_(Convex Hull) = 2sqrt(3)(n - 1) + p(1 - 1/2 sqrt(3)) + π(sqrt(3) - 1). Furthermore, the actual area equals this value iff the packing is a Groemer packing. The theorem was proved in 1960 by Helmut Groemer.
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