The pilot and pilot-rated passenger rented the airplane for a personal cross-country flight to build flight time. The trip consisted of a 261-nautical mile (nm) leg, a refueling stop, and a 271-nm leg. After completing the first leg, the airplane was refueled with 25 gallons of aviation fuel. During the second leg, as the airplane reached a position about 10 nm from the destination airport, the engine lost power. The pilot restarted the engine, and it ran for a few minutes before losing power again. The pilot was unfamiliar with the area and did not see the destination airport until the airplane was directly over the airport. He realized the airplane was "too high" and added full flaps and "started to side-slip the airplane to lose our excessive altitude." Initially, the pilot maneuvered the airplane for a landing on runway 06; however, he was still too high, so he executed a 180-degree turn and landed on runway 24. The airplane touched down near the end of the runway, overran the runway, and encountered an embankment. The right wing sustained structural damage. Federal Aviation Administration (FAA) personnel examined the airplane and reported that the fuel tanks were intact, the left wing fuel tank was dry, and the right wing fuel tank contained about 0.5 gallons of fuel. The fuel capacity of the airplane was 26 gallons, with 24.5 gallons of usable fuel.