Question

Volume de um prisma triangular regular, em que a altura mede 12cm e altura da base 4cm

Answer 1

$\boxed{\begin{array}{l}\underline{\rm C\acute alculo~da~\acute area~da~base:}\\\sf trata-se~de~calcular~a~\acute area~do~tri\hat angulo~~equil\acute atero.\\\sf para~isso~podemos~usar~a~equac_{\!\!,}\tilde ao~ A=\dfrac{\ell^2\sqrt{3}}{4}\\\sf sendo~\ell~o~lado~do~tri\hat angulo\\\sf que~neste~caso~vale~12~cm.\\\sf A=\dfrac{12^2\sqrt{3}}{4}=\dfrac{144\sqrt{3}}{4}=36\sqrt{3}~cm^2.\end{array}}$

$\boxed{\begin{array}{l}\underline{\rm c\acute alculo~do~volume}\\\sf Basta~multiplicar~a~\acute area~da~base\\\sf calculada~anteriormente~pela~altura\\\sf matematicamente~V=B\cdot h\\\sf onde~B~\acute e~a~\acute area~da~base\\\sf e~h~a~altura~do~prisma.\\\sf V=36\sqrt{3}\cdot4\\\sf V=144\sqrt{3}~cm^3\end{array}}$