Mathematics Question and Solution
Let the single side length of the regular hexagon be 1 unit.
Therefore;
Area Regular Hexagon is;
(6*1)/(4tan(180/6))
= ½(3√(3)) square units.
Area Blue/Shaded is;
2(area triangle with two equal length ⅓(2√(3)) units and angle 120°, the angle they form).
= 2(½(⅓(2√(3)))²sin120)
= 2(½(12/9)sin120)
= ⅓(2√(3)) square units.
Therefore shaded/blue area fraction is;
Area Blue ÷ Area Regular Hexagon.
= ⅓(2√(3)) ÷ ½(3√(3))
= (⅔)÷½(3)
= 4/9
