How to paint around letters?

Hi all,

I hope your day is going well, and thanks in advance for any help. I "created" a letter using curvature tool and there are 2 closed paths as well as 2 open paths intersecting the first. I then have a closed rectangular path (drawn using pen tool) directly aligned with the artboard boundaries. How do I then fill the entire rectangle minus the edge boundary of the letter? I tried live paint but I don't think that was the desired result, unless I missed a step.

Can anyone please walk me through this? 

Many thanks,

jricha38