AD=0,5*AC=\frac{3}{2}\\\\CD^2=AC^2-AD^2=9-2\frac{1}{4}=6\frac{3}{4}=>CD=\sqrt\frac{27}{4}=\frac{3\sqrt3}{2}\\S=\frac{3}{2}*\frac{3\sqrt3}{2}=\frac{9\sqrt3}{4}" alt="\angle ACD=30^0=>AD=0,5*AC=\frac{3}{2}\\\\CD^2=AC^2-AD^2=9-2\frac{1}{4}=6\frac{3}{4}=>CD=\sqrt\frac{27}{4}=\frac{3\sqrt3}{2}\\S=\frac{3}{2}*\frac{3\sqrt3}{2}=\frac{9\sqrt3}{4}" align="absmiddle" class="latex-formula">