Mathematics Question and Solution
Let the side length of the bigger regular pentagon be 1 unit.
a = ⅕*180(5-2)
a = 108°
a is the single interior angle of the regular pentagon.
b² = 2-2cos108
b = 1.6180339887 units.
c = 108-½(180-108)
c = 108-36
c = 72°
sin(0.5*108) = (0.5*1)/d
d = 0.6180339887 units.
d is the side length of the smaller regular pentagon.
Area Blue is;
0.5*1.6180339887*1sin72 - 0.5*1.6180339887*0.6180339887sin36
= 0.7694208843-0.2938926261
= 0.4755282582 square units.
e = 108+36
e = 144°
Are Red is;
0.5*0.6180339887*1.6180339887sin72
= 0.4755282581 square units.
Therefore;
Area Red ÷ Area Blue is;
0.4755282581÷0.4755282582
= 1
