Consider a paper in the shape of an equilateral triangle $A B C$ with circumcenter $O$ and perimeter 9 units. If we fold the paper in such a way that each of the vertices $A , B , C$ gets identified with $O$, then the area of the resulting shape in square units is:\\
(A) $\frac { 3 \sqrt { 3 } } { 4 }$\\
(B) $\frac { 4 } { \sqrt { 3 } }$\\
(C) $\frac { 3 \sqrt { 3 } } { 2 }$\\
(D) $3 \sqrt { 3 }$.