Question Number 105985 by Algoritm last updated on 02/Aug/20
Answered by mr W last updated on 02/Aug/20
$${r}+\frac{\mathrm{2}}{\:\sqrt{\mathrm{3}}}{r}=\frac{\mathrm{6}}{\:\sqrt{\mathrm{3}}} \\ $$$${r}=\frac{\mathrm{6}}{\mathrm{2}+\sqrt{\mathrm{3}}}=\mathrm{6}\left(\mathrm{2}−\sqrt{\mathrm{3}}\right) \\ $$$${S}=\pi{r}^{\mathrm{2}} =\mathrm{36}\left(\mathrm{7}−\mathrm{4}\sqrt{\mathrm{3}}\right)\pi \\ $$