Question

un patrat si un hexagon regulat sunt inscrise in acelasi cerc C(o.R) daca a6=9 cm aflati a:R b:A6 c:l4 d:a3 nu inteleg ajutatima va rog

Answer 1

[tex]\it a_6=\dfrac{R\sqrt3}{2} = 9 \Rightarrow R=9\cdot\dfrac{2}{\sqrt3} = \dfrac{9\cdot2\sqrt3}{3} = 6\sqrt3\ cm \\ \\ \\ \ell_6=R = 6\sqrt3 \ cm \\ \\ \\ \mathcal{A}_{hex} = 6\cdot\dfrac{\ell^2\sqrt3}{4} = 6\cdot\dfrac{(6\sqrt3)^2\sqrt3}{4} =6\cdot\dfrac{36\cdot3\sqrt3}{4} = 162\sqrt3\ cm^2[/tex]

[tex]\it \ell_4 = R\sqrt2 = 6\sqrt3\cdot\sqrt2 =6\sqrt6\ cm \\ \\ \\ a_4 = \dfrac{\ell_4}{2} = \dfrac{6\sqrt6}{2} = 3\sqrt6\ cm[/tex]