Question

un triunghi echilateral si un hexagon regulat sunt inscrisse in acelasi cerc C(O,R) . daca A3=72 radical 3 cm patrati , aflati : a) raza ; b) l3 ; c) a6

Answer 1

[tex]\it \mathcal{A}_{\Delta} =\dfrac{\ell^2\sqrt3}{4} =72\sqrt3 \Rightarrow \dfrac{\ell^2}{4} =72 \Rightarrow \ell^2 =4\cdot72 =4\cdot36\cdot2 \Rightarrow \\\;\\ \\\;\\ \Rightarrow \ell_3 = 2\cdot6\cdot\sqrt2 =12\sqrt2 cm[/tex]

$\it R = \dfrac{\ell_3\sqrt3}{2} \cdot\dfrac{2}{3} = 4\sqrt6 cm$


$\it a_6 = \dfrac{R\sqrt3}{2} =\dfrac{4\sqrt6\cdot\sqrt3}{2} =2\sqrt6\sqrt3=2\sqrt{18}=2\cdot3\sqrt2=6\sqrt2 cm$