# Star inside pentagon

Geometry Level 4

The picture above shows a regular pentagon $$ABCDE$$, with area of $$T$$. Five equilateral triangles of side length $$AB$$ were constructed inside the pentagon, example the triangle $$ABF$$. The overlapping regions were shaded, and its area is denoted as $$U$$.

Find $$\displaystyle \left \lfloor \frac{1000U}{T} \right \rfloor$$.

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