Split quadrilateral into sub-regions of a maximum area
You could recursively split the quad in half on the long sides until the resulting area is small enough.
It is pretty easy to split a rectangle/square into smaller regions and enforce a maximum area of each sub-region.  You can just divide the region into regions with sides length sqrt(max_area) and treat the leftovers with some care.
With a quadrilateral however I am stumped.  Let's assume I don't know the angle of any of the corners.  Let's also assume that all four points are on the same plane.  Also, I don't need for the the small regions to be all the same size.  The only requirement I have is that the area of each individual region is less than the max area.
Is there a particular data structure I could use to make this easier?
Is there an algorithm I'm just not finding?
Could I use quadtrees to do this?  I'm not incredibly versed in trees but I do know how to implement the structure.
I have GIS work in mind when I'm doing this, but I am fairly confident that that will have no impact on the algorithm to split the quad.