There really isn't a clear cut answer.  It depends where you live (climate,) season, whether you have heat for them in the coop, and how well they feather out, whether they have spent time outdoors, and I'm sure other factors.  The last time I brooded chicks was in the coop, in spring with one lone heat lamp, which they avoided after 3 weeks, even though night lows were well below 70.  4-8 weeks is probably a decent range of when they are fully feathered, which is when they can tolerate most any weather, though 6 weeks is probably plenty unless you live in Alaska and it's spring.  They do seem to feather out faster if they grow up outdoors.  If you brood indoors, it's a good idea to take them outdoors a while, even when quite young for short periods.  Probably the biggest mistake newbies make with heat is getting them too hot. 
 
They don't need a small area at all, they just need to have a place to get warm when they want.  Here is one chart of the minimum amount of space they do best in, to give an idea:
 
up to 2 weeks:  .5 sq ft per chick
2-4 weeks:  1 sq fr per chick
5-8 weeks: 2.5 sq ft per chick
then 4 sq ft per chick