Check out https://www.habitat.org/restores/donate-goods if the area rugs are in good shape. Your local waste area drop site may take carpeting and carpets but it is best to call. If it must go in the trash, most likely it will have to be cut up to dispose of. Companies like Junk Luggers will donate into is vast listing of charities where possible, textile recycle and dump only as a last resort. Junk Luggers (https://www.junkluggers.com/locations.html) is a fee-based pickup of items but will seek to get as much donated as possible.