Consider a circle with center \( O \) and radius \( 5 \). Points \( P \) and \( Q \) are diametrically opposite on the circle, and the line segment \( PQ \) is a diameter. A point \( R \) lies on the circle such that the line segment \( PR \) is perpendicular to \( PQ \). If \( R \) is reflected over the line \( PQ \) to obtain a point \( S \), find the area of the quadrilateral \( PORQ \). Let's think step by step and output the final answer within \boxed{}.
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