Question

A base da pirâmide é um hexágono regular que tem 6 cm de lado. Se a altura da pirâmide mede 5 cm, então a aresta lateral mede :
a) √ 30
b) 11
c ) √61
d) 30
e) 7​

Answer 1

$\boxed{\begin{array}{l}\sf a_p\longrightarrow ap\acute otema~da~pir\hat amide\\\sf h\longrightarrow altura~da~pir\hat amide\\\sf a\longrightarrow aresta~da~base\\\sf m\longrightarrow ap\acute otema~da~base\\\sf \ell\longrightarrow aresta~lateral\\\begin{cases}\sf a=6~cm\\\sf h=5~cm\end{cases}\\\sf m=\dfrac{6\sqrt{3}}{2}=3\sqrt{3}~cm\\\sf h^2+m^2=a_p^2\\\sf 5^2+(3\sqrt{3})^2=a_p^2\\\sf a_p^2=25+27\\\sf a_p^2=52~cm\end{array}}$

$\Large\boxed{\begin{array}{l}\sf \ell ^2=\bigg(\dfrac{a}{2}\bigg)^2+a_p^2\\\sf \ell^2=\bigg(\dfrac{6}{2}\bigg)^2+52\\\sf \ell ^2=9+52\\\sf \ell^2=61\\\sf \ell=\sqrt{61}~cm\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~c}}}}\end{array}}$