Question

Prisma dreapta ABC A prim B prim C prim are la baza un triunghi echilateral cu aria de 9 radical din 3 cm2 si aria unei fete laterale de 60 cm2. Aflati inaltimea prismei

Answer 1

$\it Not\breve am\ latura\ bazei\ cu\ \ell.\\ \\ \mathcal{A}_{ABC}=\dfrac{\ell ^2\sqrt3}{4}=9\sqrt3|_{:\sqrt3} \Rightarrow \dfrac{\ell ^2}{4}=9 \Rightarrow \ell ^2=4\cdot9=36=6^2 \Rightarrow \ell =6cm$

$\it Not\breve am\ \hat\imath n\brve a l\c{\it t}imea\ prismei\ cu \ \ h.\\ \\ Dimensiunile\ oric\breve arei\ fe\c{\it t}e\ laterale\ sunt\ \ell\ \d si\ \ h.$

Aria unei fețe laterale este:

$\it \ell\cdot h=60 \Rightarrow 6\cdot h=60 \Rightarrow h=10\ cm$