Let's try some geometry

Geometry Level 3

\(S.ABCD\) is a pyramid with \(S\) is the apex. The base \(ABCD\) is a square. The face \(SAB\) is an isosceles triangle with \(SA=SB\). \((SAB)\bot (ABCD)\). The angle between plane \((SCD)\) and plane \((ABCD)\) is \({60}^{o}\). The distance between plane \((SCD)\) and straight line \(AB\) is \(3\). What is the volume of the pyramid \(S.ABCD\)?

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