Hexagon in a Hexagon

Probability Level 4

ABCDEFABCDEF is a regular hexagon with side length 434.4\sqrt[4]{3}. Points G,H,I,J,K,LG,H,I,J,K,L are chosen uniformly at random, one from each side of the hexagon. What is the expected area of hexagon GHIJKL?GHIJKL?

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