Are red giants smaller than when they were main sequence stars?
No, they are much larger than when they were main sequence stars.
The Red giant stage is the second stage in the life cycle of a star (typical normal sized star), more massive stars will change to Red super giants and less massive will stay as they are as we do not yet know what's gonna happen to them since their lifetime is almost a trillion years.
Coming back to the question. A Star normally fuses hydrogen into helium, this is the main sequence stage and the star is said to be in hydro static equilibrium since the energy from the fusion reactions counteracts the gravity trying to collapse the Star.
So, when the Star runs out of it's initial reservoir of hydrogen fuel, the core collapses due to gravity, the temperature and pressure suddenly become adequate for helium fusion that is already present in the core of the star from hydrogen fusion, as the star starts to burn helium it produces even more energy than it produced while burning hydrogen, it's outer layers expand though it's temperature decreases. The Star now becomes a Red Giant and it is mostly more than 10 times larger than when it was in it's main sequence stage.
Our Sun is in it's main sequence stage burning hydrogen for 4.5 billion years and it will continue to do so for approximately the same amount of time in the future. The size of our Sun right now is about 0.2 AU. When the Sun becomes a Red giant it is estimated that it's size will reach 2 AU.