**Category:** Geometry  
**Subtype:** Solid Geometry (specifically, pyramids)  
**Problem Description:** Calculate the radius \(R\) of the circumcircle (circumscribed sphere) of the pyramid \(S.ABCD\) with a rectangular base \(ABCD\), where the dimensions of the base are \(AB = 3a\), \(BC = 4a\), and the height \(SA = 12a\) is perpendicular to the base.