Mathematics Question and Solution
Let the side of the regular hexagon which is equal the side of the square be 1 unit.
a = ½(180-108)
a = 36°
tan36 = b/0.5
b = 0.363271264 unit.
Area Blue is;
0.5*0.363271264*0.5
= 0.090817816 square units.
c² = 2-2cos120
c = 1.73205080757 units.
d = c-1
d = 0.73205080757 unit.
sin54 = e/f
f = 1.2360679775e
It implies;
f+e = d
1.2360679775e+e = 0.73205080757
e = 0.32738307374 unit.
Where e is the radius of the inscribed circle.
Area Lilac (inscribed circle) is;
π(0.32738307374)²
= 0.33671488579 square units.
Area Blue ÷ Area Lilac to 2 decimal places is;
0.090817816÷0.33671488579
= 0.26971725882
≈ 0.27
