Question

aflat aria unui cerc inscris in triunghiul echilateral de arie 9 radical din 3 cm patrati

Answer 1

$A_{\Delta} = \frac{l ^{2} \sqrt{3} }{4} \Leftrightarrow 9 \sqrt{3}= \frac{l^{2} \sqrt{3} }{4} \Rightarrow 36= l^{2} \Rightarrow l=6~(cm). \\ \\ r= \frac{ l\sqrt{3} }{6}= \frac{6 \sqrt{3} }{6}= \sqrt{3}~(cm). \\ \\ \boxed{A _{cerc}= \pi r^{2} = 3 \pi ~(cm)^{2}}.$