Question

Calcule a área lateral, a área total e o volume de uma pirâmide quadrangular regular de 7 cm de altura, cuja aresta da base é 10 cm.

Answer 1

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$\boxed{\begin{array}{l}\underline{\rm c\acute alculo~do~ap\acute otema~da~base\!:}\\\sf m=\dfrac{10}{2}\\\sf m=5~cm\\\underline{\rm c\acute alculo~do~ap\acute otema~da~pir\hat amide\!:}\\\sf a_p^2=m^2+h^2\\\sf a_p^2=5^2+7^2\\\sf a_p^2=25+49\\\sf a_p^2=74\\\sf a_p=\sqrt{74}~cm\\\underline{\rm c\acute alculo~da~\acute area~da~base\!:}\\\sf B=10^2=100~cm^2\\\underline{\bf \acute area~lateral\!:}\\\sf A_l=4\cdot\dfrac{1}{2}\cdot10\cdot\sqrt{74}\\\sf A_l=20\sqrt{74}~cm^2\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\bf \acute area~total\!:}\\\sf A_t=B+A_l\\\sf A_t=100+20\sqrt{74}\\\sf A_t=20(5+\sqrt{74})~cm^2\\\underline{\bf volume\!:} \\\sf V=\dfrac{1}{3}\cdot B\cdot h\\\sf V=\dfrac{1}{3}\cdot100\cdot7\\\sf V=\dfrac{700}{3}~cm^3\end{array}}$