Geometry Question by Mithil Shah # 6

In $\triangle ABC$ , perpendiculars $BM$ and $CN$ are drawn to tangent at $A$ to the circumcircle of $\triangle ABC$ . The tangent at $A$ meets $BC$ produced at $D$ . If $BC = 5$ , the shorter perpendicular $CN = 6$ and $AD = 5\sqrt6$ , find the area of the trapezoid $BCNM$ .