Let a be the radius of the inscribed half circle.
b = (12+a) units.
c = (12-a) units.
It implies;
(12+a)² = 12²+(12-a)²
144+24a+a² = 144+144-24a+a²
48a = 144
4a = 12
a = 3 units.
Or
a = ½*½(12)
a = ¼(12)
a = 3 units.
Again, a is the radius of the inscribed green half circle.
Area green inscribed half circle is;
½*πa²
= 0.5π(3²)
= ½(9π) square units.
= 4.5π square units.
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