Mathematics Question and Solution
Let the single side length of the equilateral hexagon be 1 unit.
Therefore;
Area blue is;
Area triangle with two sides 1 unit each, and angle 120° + Area triangle with base ½ units and height √(3) units.
= ½(sin120) + ½(½*√(3))
= ¼√(3) + ¼√(3)
= ½√(3) square units.
= 0.5√(3) square units.
Calculating area red.
It is;
Area irregular pentagon with sides ½ units, 1 unit, 1 unit, 1 unit and ½√(13) units - Area triangle with side 1 unit and ¼√(13) units, and angle (30-atan(1/2√(3)))° - Area triangle with side ½ units and ¼√(13) units, and angle (90+atan(1/2√(3)))° - Area triangle with side ¼√(21) units and 1 unit, and angle 70.893394649°
= √(3) - 0.43301270189 - 0.21650635095 - 0.54126587737
= 0.5412658774 square units.
Therefore;
Area Blue ÷ Area Red is;
(0.5√(3)) ÷ 0.5412658774
= 1.5999999999
= 1.6
= 16/10
= 8/5
