$\,A_{\large f}\,\longrightarrow\,\mbox{Área de uma face}\,$
$\,A_{\large t}\,\longrightarrow\,\mbox{Área total}\,$
$A_{\large f}\,=\,2\centerdot \dfrac{a^{\large 2}\sqrt3}{4}\,\Longrightarrow\;$ $\,A_{\large f}\,=\,\dfrac{a^{\large 2}\sqrt3}{2}\,$
$\,A_{\large t}\,=\,6\centerdot A_{\large f}\,=\,6\centerdot \dfrac{a^{\large 2}\sqrt3}{2}\,\Longrightarrow$
$\,\boxed{\,A_{\large t}\,=\,3a^{\large 2}\sqrt3\,}$