Step 1: Projection Formula:
For a triangle whose projections on the coordinate planes have areas $A_{xy},A_{yz},A_{zx}$, the area is $\sqrt{A_{xy}^2+A_{yz}^2+A_{zx}^2}$.
Step 2: Projections:
On the xy-plane the triangle projects to the triangle with legs 2 and 3: area 3. On the yz-plane, legs 3 and 4: area 6. On the zx-plane, legs 4 and 2: area 4.
Step 3: Combine:
$\sqrt{9+36+16}=\sqrt{61}$. Option (C).
Final Answer:
Option (C).
\[ \boxed{\text{(C) } \sqrt{61}} \]