The student pilot reported that she was on a solo cross-country flight and had entered the airport traffic pattern. While on the base leg, she slowed the gyroplane to follow an airplane that was established on final approach. She then turned final after the airplane had landed, however, the airplane did not exit the runway as she had anticipated. She slowed the gyroplane further and allowed a “slow vertical descent” for additional spacing from the airplane. The pilot then noticed that she had allowed the airspeed and altitude to decay. She attempted to recover by applying full throttle, however, the gyroplane turned right into a grass area and impacted terrain about 250 ft from the approach end of the runway. The rotor blades, fuselage, keel, and rudder were substantially damaged. The pilot reported that there were no preaccident mechanical malfunctions or failures that would have precluded normal operation.