Mathematics Question and Solution
Let the square side be 1 unit.
Area Square is;
1² = 1 square unit.
Calculating Area Blue.
a = 108-60-36
a = 12°
b = 180-12-108
b = 60°
1 = 2c²-2c²cos108
1 = 2.6180339887c²
c = 0.6180339887 units.
c is the side length of the regular pentagon.
(0.6180339887/sin60) = (d/sin12)
d = 0.148374968 units.
Area Blue is;
0.5sin30 - 0.5*0.148374968*0.6180339887sin108
= 0.25-0.043606309
= 0.206393691 square units.
It implies;
Area Blue ÷ Area Square to 2 decimal places is;
0.206393691÷1
= 0.206393691
= 0.21
