Mathematics Question and Solution
Let the two congruent blue semi circle's radius be a.
1 = πb²
b² = 1/π
b = √(1/π) units.
b is the radius of the yellow circle.
tanc = a/2a
c = atan(½)°
d = 2c
d = 2atan(½)°
sin(atan(½)).= √(1/π)/e
e = 1.261566261 units.
f = e+b
f = 1.261566261+√(1/π)
f = 1.8257558445 units.
It implies
(a+1.8257558445)² = (2a)²+a²
a²+3.651511689a+3.3333844037 = 5a²
4a²-3.651511689a-3.3333844037 = 0
Resolving the above quadratic equation.
a = 1.47707 units.
Again, a is the radius of the two congruent blue semi circle
Notice, the two blue congruent semi circles with equal radius will make a circle.
It implies;
Area Blue (a circle) is;
πr²
= π(1.47707)²
= 6.8541251139 square units.
