For a periodic waveform, the area above the horizontal axis is positive while the area below the horizontal axis is negative. The result is that the average or mean value of a symmetrical alternating quantity is therefore zero, (0) because the area above the horizontal axis (the positive half cycle) is the same as the area below the axis (the negative half cycle) and thus cancel each other out. This is because when we do the maths of the two areas, the negative area cancels out the positive area producing zero average voltage
Definition: The average of all the instantaneous values of an alternating voltage and currents over one complete cycle is called Average Value.