Properties of bisector from trapezoid

[dea]

A triangle as an example the bisector not through the center of figure plane. I'm interesting on trapezoid. We know that by Intermediate value theorem guarantee that there is infinite line can divide trapezoid to be two equal area. I confused the properties and how to generalization ensure that the line will divide trapezoid be two equal area.

 

[Dr.Peterson]

A triangle as an example the bisector not through the center of figure plane. I'm interesting on trapezoid. We know that by Intermediate value theorem guarantee that there is infinite line can divide trapezoid to be two equal area. I confused the properties and how to generalization ensure that the line will divide trapezoid be two equal area.

Evidently you are referring in part to this post from a year ago.

It is not clear, however, exactly what you want to do. What properties confuse you? How are you planning to define the line? What have you tried?

Also, are you defining "trapezoid" as having a pair of parallel sides (as we do in the U.S.), or not? Your example suggests the former.

Given a particular trapezoid, you could fix a point on one side, define a variable point on another side (typically the opposite side) and find the area of the figure on one side of the resulting segment. This will not be easy, in general; it will be much easier if you take the two points on parallel sides. Or are you trying to do something more general than that, or more specific?