Question

O piramida triunghiulara regulata are volumul egal cu 3$<var>\sqrt{3}</var>$ cm cubi si inaltimea de 1 cm. Aflati latura bazei.

Answer 1

$V=\dfrac {A_b\cdot h}{3}\Rightarrow3\sqrt3=\dfrac{A_b}{3}\Rightarrow A_b=9\sqrt3\ cm.$

Baza find triunghi echilateral, avem
$A_b=\dfrac{l^2\sqrt3}{4}\Rightarrow 9\sqrt3=\dfrac{l^2\sqrt3}{4}\Rightarrow l^2=36\Rightarrow l=6\ cm.$