Calculating Area Blue.
Let x be the radius of the ascribed quarter circle.
a²+5² = x²
a = √(x²-25) units.
a is the diameter of the inscribed circle.
b = ½(a)
b = ½√(x²-25) units.
b is the radius of the inscribed circle.
Area Blue is;
Area quarter circle with radius x units - Area circle with radius ½√(x²-25) units.
= ¼(x)²π-(½√(x²-25))²π
= ¼(πx²)-(¼(πx²)-¼(25π))
= ¼(25π) square units.
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