Projection is not the same as realized

Geometry Level pending

Suppose \(A, B, C\) and \(D\) are 4 points in space that lie on the same plane, with \(ABCD\) being a quadrilateral. There are 2 perpendicular planes \(\Pi_1\) and \(\Pi_2\), such that the orthogonal projections of \(ABCD\) onto these planes form a square of area \(123\) each. If \(|AB|=12,\) what is the perimeter of \(ABCD\) (to 1 decimal place)?

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