2010015606

The rectangular box \( ABCDA'B'C'D' \) has edges of lengths \( |AB|=4\sqrt3\,\mathrm{cm} \) and \( |BC|=8\,\mathrm{cm} \). The point \(S\) is the center of the lateral face \(ADD'A'\) (see the picture) and the length of the line segment \(B'S\) is \(10\,\mathrm{cm}\). Find the distance between the points \(A\) and \(A'\).