Is the center line of a triangle, one * * * three.
Reason: The midline of the triangle divides the triangle into two triangles with the same base height and area.
If there are no conditions, it seems to be of little value to study the area bisector.
There are countless area bisectors of parallelogram, which intersect with any straight line at the diagonal intersection. The reason is that the parallelogram is a centrally symmetric figure.