(Please don't top-post. Instead, place each part of your reply
immediately below the bit that it's replying to, and trim out
any bits that you're not replying to.)
Probably. Look at the numbers: /var isn't even 50% full, and the
other partitions (including /usr and /home which are the big ones)
aren't even 15% full.
Everything that's not in one of the other partitions is in the /
partition. Try this:
# du -x / | sort -n -r > /tmp/usage.txt
This will list every directory in the / partition, starting with
the ones whose files consume the most space. If you want to list
files as well as directories, then change 'du' to 'du -a'.