Question

A medida respectiva do lado e o apótema de um hexágono regular inscrito em uma circunferência de 50 cm de raio é:

a) 50; 25√3
b) 50; √3
c) 25; 50√3
d) 50; 50√3

Answer 1

$\large\boxed{\begin{array}{l}\underline{\sf Observe\,a\,figura\,que\,eu\,anexei}\\\rm No\,hex\acute agono\,inscrito\\\rm valem\,as\,seguintes\,relac_{\!\!,}\tilde oes:\\\rm \ell=R~e~~a=\dfrac{R\sqrt{3}}{2}\\\rm sendo\\\rm \ell\longrightarrow lado\,do\,hex\acute agono\,inscrito\\\rm R\longrightarrow Raio\,da\,circunfer\hat encia\end{array}}$

$\large\boxed{\begin{array}{l}\sf dados\begin{cases}\rm \ell=?\\\rm a=?\\\rm R=50\,cm\end{cases}\\\underline{\sf soluc_{\!\!,}\tilde ao\!:}\\\rm \ell=R\\\rm \ell=50\,cm\\\rm a=\dfrac{R\sqrt{3}}{2}\\\\\rm a=\dfrac{50\sqrt{3}}{2}\\\\\rm a=25\sqrt{3}\,cm\\\huge\boxed{\boxed{\boxed{\boxed{\rm\dagger\red{\maltese}~\blue{alternativa~a}}}}} \end{array}}$