You'd doing it again.
You are removing the top and bottom parts of the current screen to turn it from 4:3 into 16:9 or 16:10 rather than adding extra screen onto the side.
As I've pointed out, (and as Microsoft and Samsung have shown) You could have the same 4:3 web browser view on screen, but then perhaps an extra sidebar area for a second program to run, say a email app or a video app, or something else to can drag/drop onto or from.
I can't help but feel as time goes on, two apps on screen, in some way is going to become a no brainer way of making tablet usage more practical. And that's going to call for a wider screen at 4:3 really is just no suitable for splitting.
I don't expect the Microsoft Surface tablets will get the split screen idea right on their 1st attempt, but really it's such an obvious thing to wish to do. Not having to copy data, close the app, open another full screen app, paste the data in, do back to the 1st app, copy some more data, reopen the 2nd app, paste more in.
Come on, even you can accept this is no sensible way to do computing.