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A Red Giant is a star that is in the last phase of its life. Red Giants usually appear red but some are orange or even yellow because of the amount of elements and chemicals inside it. Red Giants have a high luminosity and a low surface temperature. I has an intermediate mass (roughly 0.3- 8 solar mass.) Hydrogen fusion reactions have become less efficient in the core region, and with gravitational collapse of the core, the fusion reactions now occur in a shell surrounding the core .This increases the luminosity of the star enormously ( up to 1000 times the Sun) and it expands. The outer layers then cool to only 3000 K or so and you get a red star, but its size is now equal to the orbit of Mercury or Venus...or even the Earth! After a few more millions of years, the star evolves into a white dwarf-planetary nebula system and then its all over for the star.
Even larger 'supergiants' can outshine the sun by over a million times. These are very massive stars seen just before their supernova stags. Betelgeuse, Antares and Arcturus are such stars. The above two images show a normal red supergiant star with most of its energy coming from a shell of hydrogen fusion activity just outside the dense core. The figure on the bottom shows an evolved red supergiant interior just before supernova.