In saturation, the current in MOSFET can be described as, $Id=uCox/2*(Vgs-Vth)^2 *W/L$. gm is derivative of Id w.r.t Vgs. In this situation , u r using same device for both cases. Hence mobility( u) , Cox , W and L must be same, use relation $gm=\sqrt{2*u*Cox*W/L*Id}$ to calculate gm when ID=820uA. Can u please tell me what do u mean by active region in MOSFET. This term is mainly used in BJT .