A topic that I have come up with, which I personally think is quite interesting, but### its feasibility is unknown.

Here is an arbitrary polygon, with each corner size ranging from 0 to 360 degrees. I hope you can find a strictly convex polygon that is completely contained within this polygon, so that the area of this convex polygon is maximized. You only need to calculate the value of this area.

Of course, since I don't have any effective methods, and I can't determine which interval corresponds to the correct method for the number of points in this polygon. But I'll give you some pictures to understand the meaning of this question.

If the two polygons given in this figure are assumed to be the same, then both extraction schemes for convex polygons may be optimal. Is there a universal construction algorithm or other technology that can solve this problem?