In the Area Manager, there should be a key icon next to each area. Click this icon, and it will give you the list of Usergroups. You can change "Can view area page", "Can view content in this area", and "Can view list of area contents" as needed to achieved the privacy level you want.
"Can view area page" only controls the landing page of that area
"Can view content saved in this area" controls viewing an actual page that is in the area
"Can view list of area contents" controls access to the list view, even if you're not allowed to open an individual page, OR if you can view the pages but don't want to show the list