Find the shaded area of ​the figure below

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Find the shaded area of ​​the figure below enter image description here

My progress $ELH: =(6+r)^2 =(12-r)^2 +(6-r)^2 \implies \boxed{r = 12(2-\sqrt3})\\ S = 144\pi(7-4\sqrt3)$

Would this resolution be correct?

enter image description here