Ken's Puzzle of the Week

Hexagon in a Square

What is the size of the largest regular hexagon that can be constructed inside a square with side-length 's'?

Source: Email from Maria del Pilar Sanchez (Another reader found this previously posted at DansMath, problem 215.)
Solutions were received from Joseph DeVincentis, Mark Rickert, Denis Borris, Keith Lynch, Earl Gose, and K Sengupta.

The largest hexagon is achieved by aligning a diameter of the hexagon along the diagonal of the square.
Then the edge of the hexagon is sqrt(2-sqrt(3)) s or about 0.518 s.
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