3. The lengths of the sides of a parallelogram are 3 and 5. The bisectors of all its internal angles limit a polygon on the plane. Find the ratio of its area to the area of the parallelogram.

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Solution. The bisectors of the internal angles of a parallelogram intersect to form a rectangle. Divide the parallelogram into rhombuses with a side length of 1 by lines parallel to the sides of the parallelogram. It is clear that the area of the red rectangle is twice the area of a rhombus with a side length of 1. And there are a total of 15 rhombuses in this parallelogram. Therefore, the ratio of the areas is $\frac{2}{15}$.