Hi Melih.
I'd like a variable-area sail since I want to do some offshore cruising, but obviously with sails a significant factor is trying to reduce the amount of variation in the vortex wake coming off the leach. A squared outline as in your sail seems likely to create a vortex, like aircraft wing flaps can;
Obviously there are some differences in that the angle of attack in your sail does not change in the same way as with a flap, but obviously the added area will change your span loading in a similar way to the flap. Unlike a plane coming in to landing we are trying to reduce vortex drag when sailing. Considering how much time we spend with twist etc trying to reduce vortex induction, adding on a piece of sail that may well create twin vortexes lower does could be a problem.
Have you considered this issue? Do you know whether it could be solved by rounding off the edges of the additional panel?