The figure ABCDEF is a cyclic hexagon with lengths AB = CD = EF = 5, BC = DE = 2 and AF = 11. Given that the area of the hexagon is 54, find the rational value of the length BE.

As usual, assume this is a competition question. You have an ample supply of paper and pens and... that's it! Of course, this

*isn't*a timed competition so that finding the answer is not so hard, but the important thing is to have a good solution method that can also be used in the future. Enjoy!

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