Mathematics Question and Solution
Let the side length of the regular pentagon be 1 unit.
a² = 2-2cos108
108° is the single interior angle of the regular pentagon.
a = 1.6180339887 units.
Area Blue is;
0.5*1*1.6180339887sin72
= 0.7694208843 square units.
Calculating Yellow Area.
b = ½(360-2(108))
b = ½(360-216)
b = ½(144)
b = 72°
cos72 = c/1
c = 0.3090169944 units.
d² = 0.3090169944²+1²-2*0.3090169944*1cos36
d = 0.7716809592 units.
(0.7716809592/cos36) = (0.3090169944/sine)
e = 13.6138224422°
f = 180-e
f = 166.3861775578°
Area Yellow is;
0.5*1*0.7716809592sin166.3861775578
= 0.3847104421 square units.
Therefore;
Area Blue ÷ Area Yellow is;
0.7694208843÷0.3847104421
= 2
