UserAgent: Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/54.0.2840.100 Safari/537.36

Steps to reproduce the problem:
This isn't really a problem, but more of a feature request. However, you can see where I am suggesting that this feature be added by:
1. Going to https://hangouts.google.com/
2. Starting a video call.
3. Hit menu, and Share screen.
Currently, there is no way to share a user-defined region of the screen.

What is the expected behavior?
It would be nice to be able to select a particular region of the desktop/screen to share in addition to the existing options.

What went wrong?
Since this is a feature request, nothing is wrong at the moment. However, this additional granularity in the screen-sharing options would really be appreciated. Please also see the images below regarding what the "Share your screen" window currently looks like, and my suggestion for how it might look

Did this work before? No 

Chrome version: 54.0.2840.100  Channel: stable
OS Version: 16.04
Flash Version: Shockwave Flash 23.0 r0

If implemented across all desktop-style platforms, (e.g. Windows 7 through 10; all current versions of Mac OS X; Linux; Chrome OS; etc...), this feature could be very useful, especially to users who use Hangouts and other simmilar platforms for teaching/tutoring and need this additional precision. Not only that, it could also potentially provide a partial work-around to Chromium  issue #437507 , which was recently re-opened as issue #660032, as well as the following posts about similar related issues:
1. https://productforums.google.com/forum/#!topic/hangouts/3-tgrHYPXlA
2. http://unix.stackexchange.com/questions/152435/sharing-your-desktop-with-google-hangouts-dual-monitor-and-gnome-shell

I would love to see this feature added to the already exemplary Google Chrome browser, and thus, would be happy to do anything in my power as a user to make that happen.