There is the concept of CATALINA_HOME and CATALINA_BASE for installing tomcat. You are obviously on some kind of unix machine, and I think tomcat was installed from this distribution.
Assuming you are using Ubuntu, check out this documentation on where to look for the directories you are looking for. They are usually distributed to fit into the unix way of browsing directories, for example. setup in / etc. The likelihood that you will find it in /var/lib/tomcat7 , but it may also be in another place, depending on your distribution.
Alternatively, run find / -name webapps to search for a directory anywhere in the file system (in the root folder).
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