A：$\frac{\sqrt{2}}{12}\mathrm{\pi }+\frac{5\sqrt{2}-\sqrt{6}}{4}$

B：$\frac{\sqrt{2}}{12}\mathrm{\pi }$

C：${\left(\frac{5\sqrt{2}-\sqrt{6}}{4}\right)}^2$

D：$\frac{{\left(\mathrm{\pi }-3\sqrt{3}+15\right)}^2}{72}$