Output the DC average value of a waveform
You say you are stuck on the 'averaging network', inbetween the squaring multiplier and the square root circuit. Averaging is usually just a low pass filter. 

Assuming you don't synchronize the filtering with your input waveform it's going to be a trade-off between output ripple and response time to changes in the input.  

Ideally you would integrate the value over an integral number of cycles of the input waveform, as you seem to be thinking (and divide by the time to get the mean), but usually that's impractical and/or unnecessary.