The instructor and student were practicing takeoffs and landings to confined areas. The student pilot performed a maximum performance takeoff from a confined area to an altitude of approximately 10 feet above the trees. During the transition to forward flight, the low rotor RPM horn sounded and the helicopter began to settle towards the trees. The instructor applied full throttle and forward cyclic. The helicopter continued to settle and the rotor RPM continued to decay. The instructor leveled the helicopter, applied full collective, and the main rotor blades contacted trees. The helicopter settled into the trees and came to rest nose down. The instructor recommended that he limit maximum performance takeoffs to large confined areas when operating above 3,000 feet density altitude. The instructor reported no mechanical malfunctions prior to the accident, and a calculated density altitude of 3,500 feet.