Parallel covering a parallelogram with squares

Suppose that \(R(h, \alpha)\) is a parallelogram with the longer side 1, with acute angle \(\alpha\) and with height h. Let S be a square with a side parallel to the longer side of \(R(h, \alpha)\) and let \(\{S_{n}\}\) be a collection of the homothetic copies of S. In this note a tight lower bound of the sum of the areas of squares from \(\{S_{n}\}\) that can parallel cover \(R(h, \alpha)\) is given.