Mathematics Question and Solution
Calculating yellow area.
2² = 2a²-2a²cos120
Where a = regular hexagon side length.
120° = single interior angle of the regular hexagon.
It implies;
4 = 3a²
a = (2/√(3)) units.
a = 1.1547005384 units.
Again, a is the side length of the regular hexagon.
b = 4-2a
b = 4-2(1.1547005384)
b = 1.6905989232 units.
Therefore;
c² = 1.6905989232²+1.1547005384²-2*1.6905989232*1.1547005384cos60
c = 1.4964366227 units.
c is the side length of one of the two equal lengths of the yellow area.
(1.4964366227/sin60) = (1.6905989232/sind)
d = 78.0675372901°
e = 360-120-2d
e = 240-2(78.0675372901)
e = 83.8649254197°
Therefore, area yellow is;
Area triangle with height 1.4964366227 units and base 1.4964366227sin83.8649254197 units - Area triangle with height 1.1547005384 units and base 1.1547005384sin120 units.
= 0.5*1.4964366227²sin83.8649254197-0.5*1.1547005384²sin120
= 1.1132486541-0.5773502692
= 0.5358983849 square units.
