Get taxonomy terms within category

We have various accommodation categories and a custom taxonomy called ‘Areas’ with main cities(parent) and suburbs(children). When a user clicks a category and gets taken to the cats page we would like to display a dropdown box(hierarchical) with the areas that is associated with the selected category. We have tried wp_dropdown_categories( $args ); but still end up with all the areas – we need only those areas within the selected category.

What is the best way to go about this? Only started working with WordPress recently.