The honeycomb

Two regular hexagons inscribed in a square. If the hexagons have side length a and b, what is the square’s side length?

Scroll down for a solution to this problem.


The square side is (a+b)5(3-√3)/4.

Solution by Jaihind Singh.


The honey comb
A shelter nice and strong
A small edifice in wax
With sweetness to taste and to eat
A nectar droping out so soft
Very buzzy are the bees
They store up the golden honey drops
While working and singing
Bumping and buzzing in the garden
Feasting in their honeycomb.


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