Let \( \overrightarrow{OA} = \vec{a} \), \( \overrightarrow{OB} = 12\vec{a} + 4\vec{b} \) and \( \overrightarrow{OC} = \vec{b} \), where \( O \) is the origin. If \( S \) is the parallelogram with adjacent sides \( OA \) and \( OC \), then \( \dfrac{\text{area of the quadrilateral } OABC}{\text{area of } S} \) is equal to _______.
