Three circles with radius 2 are mutually tangent. What is the total area of the circles and the region bounded by them, as shown in the figure? [asy]
filldraw((0,0)--(2,0)--(1,sqrt(3))--cycle,gray,gray);
filldraw(circle((1,sqrt(3)),1),gray);
filldraw(circle((0,0),1),gray);
filldraw(circle((2,0),1),grey);
[/asy]<spanclass=′latex−bold′>(A)</span>10π+43<spanclass=′latex−bold′>(B)</span>13π−3<spanclass=′latex−bold′>(C)</span>12π+3<spanclass=′latex−bold′>(D)</span>10π+9<spanclass=′latex−bold′>(E)</span>13π