Start from Heptagon to Triangle!

$ABCDEFG$ is an equilateral heptagon. Segment $AE$ is also a side of an equilateral hexagon named $AEHIJK$ . Segment $AH$ is also a side of an equilateral pentagon named $AHLMN$ . Segment $AL$ is also a side of a square, named $ALOP$ . Diagonal $AO$ is also a side of an equialteral triangle, named $AOQ$ . If $BC = 4 \space cm$ , find the length of $AQ$ in $cm$ . Round your answer to two decimal places.

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