I am having a hard time understanding what you are trying to do. It would be helpful if you could post some simple code to demonstrate what you have and how it fails to do what you want.
I don't know a way of forcing a MainWindow to display less than the available widgets. Is that what you are trying to do? And if so, then why?
The "title bar" for the main window is normally a constant "set it once" deal and is usually the name of your application. In any event you know what that title is because you set it!
The normal way to do what it sounds like you want is to make a new top level window with a new title for that window and probably a label for the file name that you have just opened.
The user and/or Tk re-sizes windows, not your program!
The Tk minimum main window size as you have already seen is in points, not lines of text or widgets, etc. There is not an easy way to figure out how that number of points relates to what is displayed upon the screen.
You can ask questions like is line #45 of this text widget visible on the screen or not? There are methods to pack and re-pack widgets and re-display the screen.
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