Editing Polygon (section)

====Self-intersecting====
The area of a [[Complex polygon|self-intersecting polygon]] can be defined in two different ways, giving different answers:
* Using the formulas for simple polygons, we allow that particular regions within the polygon may have their area multiplied by a factor which we call the ''density'' of the region. For example, the central convex pentagon in the center of a pentagram has density 2. The two triangular regions of a cross-quadrilateral (like a figure 8) have opposite-signed densities, and adding their areas together can give a total area of zero for the whole figure.<ref>{{cite journal|url=http://dynamicmathematicslearning.com/crossed-quad-area.pdf|title=Slaying a geometrical 'Monster': finding the area of a crossed Quadrilateral|last=De Villiers|first=Michael|journal=Learning and Teaching Mathematics|volume=2015|issue=18|date=January 2015|pages=23–28}}</ref>
* Considering the enclosed regions as point sets, we can find the area of the enclosed point set. This corresponds to the area of the plane covered by the polygon or to the area of one or more simple polygons having the same outline as the self-intersecting one. In the case of the cross-quadrilateral, it is treated as two simple triangles.{{citation needed|date=February 2019}}