Despite its cooler surface, why is a red giant vastly more luminous than it was on the main sequence?

Answer

The immense increase in surface area allows for greater total energy radiation

While the surface temperature drops, the star expands enormously (potentially by a factor of hundreds). This massive increase in surface area causes the total energy radiated (luminosity) to increase significantly.

Despite its cooler surface, why is a red giant vastly more luminous than it was on the main sequence?
astronomystarstellar evolutionmain-sequencered giant