On June 3, 2024, about 1055 eastern daylight time, a Cessna 172K, N78445, was substantially damaged when it was involved in an accident near Terryville, Connecticut. The student pilot sustained minor injuries. The airplane was operated as a Title 14 Code of Federal Regulations Part 91 instructional flight. The student pilot reported that the airplane’s fuel tanks were full before her departure on a solo cross-country flight. About halfway during the flight, at 5,500 ft mean sea level, the engine rpm began to decrease until the engine lost all power, and the propeller was not windmilling. She then tried to restart the engine, but the propeller would not turn. The student pilot reported that she applied carburetor heat after the loss of engine power. The student pilot then diverted and attempted to glide the airplane to a nearby airport, but it impacted wooded terrain about 1 mile from the airport. Review of a Federal Aviation Administration (FAA) carburetor icing chart revealed a risk of “Serious Icing – glide power” for the reported temperature and dew point. Examination of the airplane by an FAA inspector revealed it came to rest inverted in a campground. Both wings and the fuselage were substantially damaged. The inspector added that about three-fourths of the total fuel capacity remained onboard, and that fuel was leaking from the wing fuel tanks that were compromised during the impact. The engine was subsequently examined at a recovery facility. Powertrain and valvetrain continuity were confirmed throughout the engine and no anomalies were noted. The engine was then started on the airframe. It started without hesitation and ran continuously at idle power. Due to airframe damage and safety concerns, higher power settings were not attempted (for more information, see Engine Examination Summary in the public docket for this investigation.)