Let the single side length of the regular hexagon be 2 unit.
Therefore;
Area Red is;
4 - ½*½(2/(√(3)+1))
= 4 - ((√(3)-1)/2)
= ½(9-√(3)) square unit.
Area Yellow is;
½(√(3)+2)(√(3)+1) - ½(√(3))
= ½(5+2√(3)) square unit.
It implies;
Area Red ÷ Area Yellow exactly as a single fraction is;
½(9-√(3)) ÷ ½(5+2√(3))
= (9-√(3))/(5+2√(3))
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