Rectangle and two equilateral triangles

Geometry Level 1

In rectangle BCEF \text{BCEF} , points G \text{G} and H \text{H} are midpoints. Equilateral triangles AGH \text{AGH} and GDH \text{GDH} are drawn. Given that BC=FE=1 \text{BC=FE=1} and BF=CE=2 \text{BF=CE=2} . Find the total area of the shaded regions rounded to three decimal places.


The answer is 1.753.

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