lissajou figure area calcuate
Though I have not used this before, I think this is how it works:
P=V*I*cosφ.
You can easily measure V and I, but how do you measure φ ?
To measure φ, the phase angle between voltage and current, you use Lissajous figures. So I would say you need to insert a low resistor in series with your load and the voltage across it will be the current information. So the resistance has to be low enough compared to the load impedance, but high enough so you can get a reasonable voltage across it.
Apply that to one of the scope inputs, preferably Y, since you can adjust ist amplitude more easily (depends on the scope). The voltage across the load is the other signal for deflection, say X.
Then, from the Lissajous figure you determine the phase angle, φ.
With that and the voltage and current measuered accurately, you get the power.
But you have to calibrate your scope first, to make sure that the measurement is accurate. The apparent amplitude of the two signals should be equal. So first apply only the voltage to the scope and record the amplitude, as accurately as you can. If you can adjust it to a certain number of divisions, that is best, if not just record it as accurately as possible. If your scope uses the X amplifier, usually you can only adjust the amplitude in a few steps. Then display only the current and adjust the amplidute (using the steps attenuator and the variable one) to exactly match the voltage amplitude you measured previously.
Then apply both the voltage and current, since you know their relative amplitudes are the same and determine the phase angle from the Lissajous figure.