Creating a new file from a rectangular region of a PDF file

I want to create a new PDF file from a rectangular region of an existing PDF file, old_file.pdf. Currently, I use the following rather laborious process:

1. Open the old_file.pdf in Preview.
2. Chose the rectangular regions using rectangular selection.
3. Copy the region using cmd c.
4. Paste the region into an empty slide in a Keynote file, using cmd v.
5. Export that single slide (by hiding all others) into a new_file.pdf.
6. Open new_file.pdf in Preview, chose and crop the rectangular region, then save the file and exit Preview.

Surely, there must be a better way. What is it?

Solution 1:

You can select the region of interest and hit copy. Then go to the file menu and select 'New from Clipboard'. A new PDF file is displayed with only your selection.

Quick workflow example...