Hi Burr, for this kind of thing you can do a "mutual trim".

That means to select both objects you want to trim, then run Edit/Trim, and at the prompt where it says to select cutting objects, just push Done (or right-click) instead of picking anything, that signals that each object will trim the other.

Here is a step-by-step which is a bit clearer:

To start with, select both pieces:



Then run Edit/Trim - the following prompt will appear:



But in this case you don't want to select any additional cutting objects, you want each of these pieces to cut the other, so push "Done" or right-click in a viewport to signal a "mutual trim" operation.

Then the next stage of Trim is that it cuts up everything, and you pick which pieces you want to discard or keep, the model will look like this:



In this particular case it happens to be easier to pick the pieces that you want to keep, rather than picking the pieces you want to discard. So to do that, you can switch to Mode: Keep, like this:



Now pick on the pieces you want to keep, the 2 big outer pieces:



Then push "Done" or right-click and the mutual trim will be complete:



Those pieces are now ready to be joined. Then after they are joined there is a planar opening on the bottom which can be sealed by picking the object and running Construct / Planar.

Hope this helps!

- Michael