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.
sin72 = b/1
b = 0.9510565163 units.
cos72 = c/1
c = 0.3090169944 units.
Area Blue is;
0.5*1*1sin108+0.5*0.3090169944*0.9510565163
= 0.6224745712 square units.
d = a-c
d = 1.6180339887-0.3090169944
d = 1.3090169943 units.
Area Yellow is;
0.5*1.3090169943*0.9510565163
= 0.6224745712 square units.
Therefore;
Blue Area ÷ Yellow Area is;
0.6224745712÷0.6224745712
= 1
