Question

Um prisma regular triangular tem 10 cm de altura. Sabendo que a medida da aresta da base é de 6 cm, determine a área total do prisma.​

Answer 1

$\large\boxed{\begin{array}{l}\underline{\rm C\acute alculo~da~\acute area~da~base~B\!:}\\\sf B=\dfrac{6^2\sqrt{3}}{4}\\\\\sf B=\dfrac{\diagdown\!\!\!\!\!\!36\sqrt{3}}{\diagdown\!\!\!\!4}\\\\\sf B=9\sqrt{3}~cm^2\\\underline{\rm C\acute alculo~da~\acute area~lateral~A_l\!:}\\\sf A_l=3\cdot6\cdot10=180~cm^2\\\underline{\boldsymbol {C\acute alculo~da~\acute area~total~A_t~do~prisma\!:}}\\\sf A_t=A_l+2\cdot B\\\sf A_t=180+2\cdot9\sqrt{3}\\\sf A_t=180+18\sqrt{3}\\\sf A_t=18\cdot(10+\sqrt{3})~cm^2\end{array}}$