Question

22. Calcule a área total de cada uma das pirâmides regulares a seguir. a) b) 5 cm 4cm 4 cm Ilustrações. Ronaldo Lucena/ID/BR 3 cm 4 cm 4 cm 3 cm​

Answer 1

$\large\boxed{\begin{array}{l}\tt a)\\\underline{\sf C\acute alculo\,do\,ap\acute otema\,da\,base:}\\\rm m=\dfrac{3}{2}\\\underline{\sf C\acute alculo\,do\,ap\acute otema\,da\,pir\hat amide:}\\\rm a_p^2=h^2+m^2\\\\\rm a_p^2=5^2+\bigg(\dfrac{3}{2}\bigg)^2\\\\\rm a_p^2=25+\dfrac{9}{4}=\dfrac{109}{4}\\\\\rm a_p=\dfrac{\sqrt{109}}{2}\\\underline{\sf C\acute alculo\,da\,\acute area\,da\,base}\\\rm B=3^2=9\,cm^2\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\sf C\acute alculo\,da\,\acute area\,lateral}\\\rm A_l=4\cdot\dfrac{1}{2}\cdot3\cdot\dfrac{\sqrt{109}}{2}\\\\\rm A_l=\dfrac{\backslash\!\!\!4\cdot3\sqrt{109}}{\backslash\!\!\!4}\\\\\rm A_l=3\sqrt{109}\\\underline{\sf C\acute alculo\,da\,\acute area\,total}\\\sf A_t=B+A_l\\\rm A_t=9+3\sqrt{109}\\\rm A_t=3\cdot(3+\sqrt{109})\,cm^2\end{array}}$

$\large\boxed{\begin{array}{l}\tt b)\\\sf A_t=a^2\sqrt{3}\\\rm A_t=4^2\sqrt{3}\\\rm A_t=16\sqrt{3}\,cm^2\end{array}}$