High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! Carthage Township is one of the fourteen townships of Athens County, Ohio, United States. The 2000 census found 1,467 people in the township. It is the only Carthage Township statewide. The township is governed by a three-member board of trustees, who are elected in November of odd-numbered years to a four-year term beginning on the following January 1.