Answer: \(\dfrac{121}{4}\).

We start with the main method. Use gradients: perpendicular lines have gradients whose product is \(-1\).

The midpoint of \(AB\) is

\(\left(\frac{1+5}{2},\frac{4+6}{2}\right)=(3,5).\)

The gradient of \(AB\) is

\(\frac{6-4}{5-1}=\frac12,\)

so the perpendicular bisector has gradient \(-2\).

Its equation through \((3,5)\) is

\(y-5=-2(x-3).\)

Hence \(y=-2x+11\).

The intercepts are \(D=(0,11)\) and \(C=\left(\frac{11}{2},0\right)\).

Therefore

\(\text{area of } \triangle OCD=\frac12\cdot\frac{11}{2}\cdot11=\frac{121}{4}.\)

This completes the solution and gives the required result.