Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the side length of the regular hexagon be 1 unit.
Area Hexagon is;
(½(6))(1/(2tan(180/6)))
= 3/2tan(30)
= ½(3√(3)) square units.
Notice;
1/sin105 = x/sin45
x = √(3)-1 unit.
y = 1.23931367493 units.
z = 1.50597117915 units.
a = 120-asin(0.81811048221)
a = 65.10390936101°
c = 54.89609063899°
d = 1.10874112934 units.
Area Red is;
Area triangle with height 1.10874112934 units and base sin60 units.
= ½*1.10874112934sin60
= (26725571√(3)/96417713) square units.
Therefore;
Area Hexagon ÷ Area Red exactly is;
(½(3√(3))) ÷ (26725571√(3)/96417713)
= 289253139/53451142
= 5.41154273187 exactly in decimal.
