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Solution:
Area of triangle ACE = Area of triangle BCE
Area = (2a)/2 = a
In triangle ABD, AB = BD,
BD = BC + CD,
\[\Rightarrow a\sqrt3 = a+2\]
\[\Rightarrow a = \frac2{\sqrt3-1}\]
\[\Rightarrow a = \sqrt3+1\]
\[\Rightarrow Area = \sqrt3+1\]
