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? $\textbf{(A)}\ 10\pi+4\sqrt{3}\qquad$ $\textbf{(B)}\ 13\pi-\sqrt{3}\qquad$ $\textbf{(C)}\ 12\pi+\sqrt{3}\qquad$ $\textbf{(D)}\ 10\pi+9\qquad$ $\textbf{(E)}\ 13\pi$
Solution
The total area can be considered as the equilateral triangle plus the three sectors each with angle $300^\circ$.
Four circles with radius $3$ have centers at the corners of a square, each tangent to its two neighboring circles. What is the total area of the circles and the region bounded by them?
$\textbf{(A)}\ 10\pi+4\sqrt{3}\qquad$ $\textbf{(B)}\ 13\pi-\sqrt{3}\qquad$ $\textbf{(C)}\ 12\pi+\sqrt{3}\qquad$ $\textbf{(D)}\ 10\pi+9\qquad$ $\textbf{(E)}\ 13\pi$ 
