During a cross-country instructional flight, the airplane experienced a total loss of engine power, and the flight instructor performed a forced landing to a road about 2 miles from the destination airport. During the landing, the airplane struck trees and came to rest upright, sustaining substantial damage to the wings and fuselage. A recovery crew responded the same day and noted that both wing fuel tanks were intact but absent of fuel. An FAA inspector subsequently examined the wreckage at the recovery facility and found no fuel in the filter at the belly sump, which was the lowest point in the fuel system. The flight instructor later reported that fuel exhaustion was the likely cause of the accident. He stated that before departure, he relied on avionics, which indicated 21 gallons of fuel onboard rather than visually verifying the fuel quantity in the wing fuel tanks, and the avionics indication was likely inaccurate.