Kind of an interesting puzzle! Maybe you could explain your use case (that is, what are you trying to accomplish). I am curious!
Here is a way to create a circular buffer, centered on the centroid of the polygon, of a specified total area outside your source polygon.
Watch your units, if you are using Shape_Area everything should be in map units or square map units (ie feet, meters).
1. Add a field of type Double to your polygon feature class. (xarea)
2. Calculate this field to the area plus your desired buffer area
3. Calculate the radius of a circle for this area, the Python expression would be (math.pi / xarea) ** 0.5
4. Convert your polygons to points with the Feature To Point tool.
5. Buffer these points using the calculated radius value.