Question

Prisma triunghiulara regulata ABCA'B'C' are aria laterala de 24√3cm si aria totala de 30√3. Aflati: L;V;Aa'bc

Answer 1

Sper că te-am ajutat! Mult noroc la școală!

Scuze de foaia de romana. Atât s-au putut la ora asta:))

Answer 2

$\it Fie\ \ \ell\ -\ latura\ bazei,\ \ h\ -\ \^{i}n \breve a \ell \c{\it t}imea\ prismei$

$\it 2\cdot \mathcal{A}_b=\mathcal{A}_t-\mathcal{A}_\ell=30\sqrt3-24\sqrt3=6\sqrt3 \Rightarrow \mathcal{A}_b=3\sqrt3\ cm^2\ \ \ \ \ (1)\\ \\ \\ Dar,\ \mathcal{A}_b=\dfrac{\ell^2\sqrt3}{4}\ \ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow \dfrac{\ell^2\sqrt3}{4}=3\sqrt3|_{:\sqrt3} \Rightarrow \dfrac{\ell^2}{4}=3 \Rightarrow\ell^2=4\cdot3 \Rightarrow \ell=\sqrt{4\cdot3} \Rightarrow\\ \\ \Rightarrow \ell=2\sqrt3\ cm\ \ \ \ (3)$

$\it \mathcal{A}_\ell=3\ell\cdot h=24\sqrt3|_{:3} \Rightarrow \ell\cdot h=8\sqrt3\ \stackrel{(3)}{\Longrightarrow} 2\sqrt3\cdot h=8\sqrt3|_{:2\sqrt3} \Rightarrow h=4\ cm$

$\it \mathcal{V}=\mathcal{A}_b\cdot h=3\sqrt3\cdot4=12\sqrt3\ cm^3$