Trigger rules can help you accomplish this. Within your VCS trigger, you can specify a collection of rules to filter in or out various conditions that will cause your build configuration to trigger. These are independent of your VCS rules and those rules will handle what you choose to checkout as normal. The rule syntax is as follows:
+|-[:[user=VCS_username;][root=VCS_root_id;][comment=VCS_comment_regexp]]:Ant_like_wildcard
The Ant_like_wildcard is the element of particular interest to you in this case, as you can use them (among other things) to filter in or out a particular directory.
Here is an example from the TeamCity Documentation:
"-:lib/**" prevents the build from triggering by updates to the "lib" directory of the build sources
Using your example, your trigger rule would look something like:
+:ProjectA/**
You can use a single inclusion rather than multiple exclusions because of the way TeamCity handles those types of rules:
When specifying the rules, please note that as soon as you enter any "+" rule, TeamCity will change the implicit default from "include all" to "exclude all".
You can find the full TeamCity VCS Trigger documentation here