Mathematics Question and Solution
Let the length of the ascribed regular hexagon be 2 units.
Therefore it area will be;
(2*2*6)/(4tan(180/6))
= 6/tan30
= 6√(3) square units.
The green areas is;
Area rectangle with length 2√(3) units and width 1 unit + Area regular hexagon with side ⅔√(3) units + Area regular hexagon with side ⅓√(3) unit.
= (2√(3)*1) + (6*(⅔√(3))²/(4tan(180/6)) + (6*(⅓√(3))²/(4tan(180/6))
= 2√(3) + 2√(3) + ½(√(3))
= 4√(3) + ½(√(3))
= ½(9√(3)) square units.
It implies;
Shaded fraction is;
Area Green ÷ Area Ascribed Regular hexagon
= ½(9√(3)) ÷ 6√(3)
= (9√(3))/(12√(3))
= ¾
