**Category:** Geometry  
**Subtype:** Solid Geometry (specifically, pyramids)  
**Problem Description:** The problem involves a pyramid (or tetrahedron) with a triangular base. It requires finding the volume of the pyramid \(B.ACED\) given specific conditions about the points \(D\) and \(E\) on the segments \(SA\) and \(SC\), respectively, and the distance \(DE\). The base triangle \(ABC\) is a right isosceles triangle, and the height from point \(S\) to the base is perpendicular.