In trapezoid \(ABCD\), sides \(AB\) and \(CD\) are parallel with lengths 10 units and 20 units, respectively, and the altitude from \(AB\) to \(CD\) is 12 units. The diagonals \(AC\) and \(BD\) intersect at point \(E\). A circle with center \(O\) passes through \(E\) and is tangent to \(AB\) and \(CD\). If \(M\) and \(N\) are the midpoints of \(AD\) and \(BC\) respectively, find the area of quadrilateral \(MENO\). Let's think step by step and output the final answer within \boxed{}.
user