Question

4) Uma pirâmide de base quadrada de lado 12cm e altura 4cm. Determine: a) Apótema da base; b) Apótema da pirâmide; c) Área da base; d) Área lateral; e) Área total; f) Volume.​

Answer 1

$\boxed{\begin{array}{l}\tt dados\begin{cases}\sf \ell=12~cm\\\sf h=4~cm\end{cases}\\\tt a) ~m=\dfrac{\ell}{2}=\dfrac{12}{2}=6~cm\\\\\tt b)~\sf a_p^2=h^2+m^2\\\sf a_p^2=4^2+6^2\\\sf a_p^2=16+36\\\sf a_p^2=52\\\sf a_p=\sqrt{52}=2\sqrt{13}~cm\\\tt c)~\sf B=\ell^2\\\sf B=12^2\\\sf B=144~cm^2\\\tt d)~\sf A_l=4\cdot\dfrac{1}{\backslash\!\!\!2}\cdot12\cdot\backslash\!\!\!2\sqrt{13}\\\sf A_l=48\sqrt{13}~cm^2\\\tt e) ~\sf A_t= A_l+B\\\sf A_t=48\sqrt{13}+144\\\sf A_t=48\cdot(\sqrt{13}+3)~cm^2\end{array}}$

$\large\boxed{\begin{array}{l}\tt f)~\sf V=\dfrac{1}{3}\cdot B\cdot h\\\\\sf V=\dfrac{1}{\diagup\!\!\!3}\cdot \diagup\!\!\!\!\!\!14\diagup\!\!\!\!\!4\cdot4\\\\\sf V= 48\cdot4\\\sf V=192~cm^3\end{array}}$