Parallel covering a parallelogram with squares

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