The cage is electrically one quarter of the operating wavelength long. It is connected to the mast at its upper end. This way it isolates the lower part of the mast (λ/4 stub) and makes the upper part of the mast the radiator. Very often the typical height of such an antenna is no problem as the height of the mast is selected for the TV or FM antennas on top.
Example: At 1000 kHz the wavelength is 300 m. Therefore the minimum length of the cage antenna is a bit more than 150 m; 75 m for the radiator, 75 m for the cage and some meters to make the lower end of the cage unaccessible from the ground as the lower end of the cage carries a very high RF voltage.