The "use more area" needs to be considered in the sense that, designed properly, they eliminate left turn lanes and "suicide lanes" in the center of the road.
Instead, with proper design, you make this "left turn" by going to the next roundabout, going around to follow the road the opposite direction, and then make a right turn.
It's also only true when compared against a no-frills intersection. A two-lane roundabout has better overall throughput than a two-lane intersection with traffic lights. To increase throughput, they usually add turn lanes to avoid cars having to stop in the through lanes -- but the turn lanes require more road surface than the roundabout would have.