Given, $\angle A=75^{\circ}, \angle B=45^{\circ}$ and $a=2(\sqrt{3}+1)$
In $\Delta A O C, \tan 60^{\circ}=\frac{x}{y} $
$\Rightarrow \sqrt{3}=\frac{x}{y}$
$\Rightarrow x=\sqrt{3} y $
Now, $ x+y =2(\sqrt{3}+1)$
$\Rightarrow \sqrt{3} y+y=2(\sqrt{3}+1)$
$ \Rightarrow y(\sqrt{3}+1) =2(\sqrt{3}+1) $
$ \Rightarrow y =2 $
$\Rightarrow x=2 \sqrt{3}$
Now, area of $\Delta A B C=$ area of $\Delta A O B+$ area of $\Delta A O C$
$=\frac{1}{2} \times x \times x+\frac{1}{2} \times x \times y=\frac{1}{2} x[x+y]$
$=\frac{1}{2} \times 2 \sqrt{3} \times 2(\sqrt{3}+1)$
$=2 \sqrt{3}(\sqrt{3}+1)$
$=6+2 \sqrt{3}$ sq units
