Editing Area (section)

==Area bisectors==
{{Main article|Bisection#Area bisectors and perimeter bisectors}}

There are an infinitude of lines that bisect the area of a triangle. Three of them are the [[Median (triangle)|medians]] of the triangle (which connect the sides' midpoints with the opposite vertices), and these are [[Concurrent lines|concurrent]] at the triangle's [[centroid]]; indeed, they are the only area bisectors that go through the centroid. Any line through a triangle that splits both the triangle's area and its perimeter in half goes through the triangle's incenter (the center of its [[incircle]]). There are either one, two, or three of these for any given triangle.

Any line through the midpoint of a parallelogram bisects the area.

All area bisectors of a circle or other ellipse go through the center, and any [[Chord (geometry)|chords]] through the center bisect the area. In the case of a circle they are the diameters of the circle.