11. In $\triangle A B C$, it is known that $A=\frac{\pi}{3}, \frac{A B}{A C}=\frac{8}{5}$, and the inradius $r=2 \sqrt{3}$. Then the area of this triangle is
Given $A B=8 k, A C=5 k$, then $B C^{2}=(64+25-40) k^{2}=49 k^{2} \Rightarrow B C=7 k$. Thus, $S_{\triangle A B C}=20 k^{2} \cdot \frac{\sqrt{3}}{2}=10 k \cdot 2 \sqrt{3} \Rightarrow k=2$, so $S_{\triangle A B C}=40 \sqrt{3}$.