Average power dissipated as the heat in the resistor
With AC the real power is



(From: https://en.wikipedia.org/wiki/Electric_power#Alternating_current)

Cosθ is 1 because you have resisitive load.

Thus you have to calculate with RMS values.

Note that power can also be calculated as

 

(From: https://en.wikipedia.org/wiki/Electric_power#Resistive_circuits)

and RMS voltage is



(From: https://en.wikipedia.org/wiki/Root_mean_square)

Thus your power is