In a written statement, the pilot reported flying into a canyon at 6,100 feet with the intent to fly over it. During the ascent the airplane started to lose airspeed and altitude. The pilot attempted to turn around, however, could not because the airplane would stall due to an insufficient amount of airspeed. The pilot initiated a forced landing into trees at the bottom of a ravine; subsequently, the airplane received substantial damage to the wings, fuselage and empennage. The pilot reported no mechanical failures or malfunctions with the airframe or engine at the time of the accident. The calculated density altitude for the conditions at 6,100 feet, altimeter setting 30.14, and temperature of 22 Degrees Celsius, is 8,238 feet. The published maximum operating density altitude for the C-172H is 13,100 feet. In a written statement, the pilot stated that the accident could have been prevented by circling over a nearby city until enough altitude was acquired to fly over the canyon.