Mathematics Question and Solution
Let the side length of the hexagon be 2 units.
a = ⅙*180(6-2)
a = 120°
b = ½(360-(30+90))
b = ½(240)
b = 120°
(2/sin45) = (c/sin15)
c = 0.7320508076 units.
Calculating Area Blue.
It is;
8(area triangle with height 2 units and base 0.7320508076sin120 units).
= 8(0.5*2*0.7320508076sin120)
= 5.0717967699 square units.
d = 2+2(2sin30)
d = 4 units.
d is the radius of the ascribed circle.
e = 2+2c
e = 3.4641016152 units.
f = 2-c
f = 1.2679491924 units.
It implies;
Area red is;
Area circle with radius 4 units - Area square with side length 3.4641016152 units - 4(area triangle with height 2 units and base 2sin120 units) - 4(area rectangle with length 3.4641016152 units and width 1.2679491924 units).
= π(4)²-3.4641016152²-4(0.5*2*2sin120)-4(3.4641016152*1.2679491924)
= 50.2654824574-12-6.9282032303-17.5692193815
= 13.7680598456 square units.
Therefore;
Red Area ÷ Blue Area is;
13.7680598456÷5.0717967699
= 2.7146316129
