how to get the active project areas by java API

From a plain java client you could do the following:

IProcessItemService service = (IProcessItemService) repository.getClientLibrary(IProcessItemService.class);
List<IProjectArea> activeProjectAreas = new ArrayList();
List<IProjectArea> allProjectAreas;
projectAreas = service.findAllProjectAreas(service.ALL_PROPERTIES,monitor);
for (Iterator<IProjectArea> iterator = projectAreas.iterator(); iterator.hasNext();) {
 IProjectArea iProjectArea = iterator.next();
 
 if (iProjectArea.isArchived()==false) {
  activeProjectAreas.add(iProjectArea)
 }
}