8. Given that $A B C D$ and $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ are two rhombuses with side lengths of $\sqrt{3}+1$. If $A C \perp A^{\prime} C^{\prime}$, $\angle A B C=\angle A^{\prime} B^{\prime} C^{\prime}=120^{\circ}$, then the perimeter of the shaded part is $\qquad$
$8$