KöMaL 2022 C1702

Vertex $A$ of a quadrilateral $ABCD$ lies on the plane $S$, its diagonal $BD$ is parallel to the plane $S$, and its vertex $C$ is at a distance of $8$ units from the plane $S$. Given that the orthogonal projection of the quadrilateral onto $S$ is a square with a diagonal $6$ units long, prove that quadrilateral $ABCD$ is a rhombus, and calculate the length of its sides.