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Solution:
Length of rectangle = x + y
\[\Rightarrow 2a\sqrt3=\sqrt{1-a^2}+\sqrt{4-a^2}\]
\[\Rightarrow a^2=\frac{5+\sqrt{13}}{16}\]
Blue Area:
\[Area = (2a)(2a\sqrt3)=4a^2\sqrt3\]
\[\Rightarrow Area = \frac{\sqrt3}4\cdot(5+\sqrt{13})\]
