The flight instructor and student pilot were practicing takeoffs and landings to confined areas. The student pilot performed a maximum performance takeoff from a confined area to an altitude of about 10 feet above the trees. During the transition to forward flight, the low rotor rpm horn sounded and the helicopter began to settle toward 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 the student 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.