Mathematics Question and Solution
Let the regular pentagon side be 1 unit.
sin72 = a/1
a = 0.9510565163 units.
Let the side of the two inscribed congruent squares be b.
c = ½(b) units.
b+½(b) = 0.9510565163
b = 0.63403767753 units.
Area Yellow is;
(0.63403767753)²
= 0.40200377653 square units.
Calculating Area Blue.
d = ½(1-0.63403767753)
d = 0.18298116124 units.
e² = 2-2cos108
e = 1.61803398875 units.
f = ½(1.61803398875-0.63403767753)
f = 0.49199815561 units.
Area Blue is;
0.5(0.49199815561+0.18298116124)0.9510565163
= 0.32097173883 square units.
Area Blue ÷ Area Yellow to 2 decimal places is;
0.32097173883÷0.40200377653
= 0.79842966054
≈ 0.80
