Question

o prisma triunghiulara regulata are l=12 cm si aria totala =360radical din3 
.Calculati: a)inaltimea prismei b)volumul prismei

Answer 1

$l=12\ cm \\ A_t=360\sqrt3 \\ \boxed{h-?} \\ \boxed{V-?} \\ \bold{Rezolvare:} \\ A_l=P_b \cdot h \ \ \ \ \Rightarrow h=\frac{A_l}{P_b} \\ A_t=A_l+2A_b \ \ \ \Rightarrow A_l=A_t-2A_b \\ A_b=l^2 \sqrt{\frac{3}{4}}=12^2\sqrt{\frac{3}{4}}=144\sqrt{\frac{3}{4}}=\sqrt{20 \ 736} \cdot \cqrt\sqrt{\frac{3}{4}} = \sqrt{\frac{62 \ 208} {4}} \\ A_b=\sqrt{15 \ 552}=72\sqrt{3} \ cm^2 \\ P_b=3l=3\cdot 12 \ cm=36 \ cm \\ h= \frac{72\sqrt{3} \ cm^2}{36 \ cm} \\ \Rightarrow \boxed{h=2\sqrt3 \ cm} \\ V=A_b \cdot h$
$V=72 \sqrt3 \ cm^2 \cdot 2 \sqrt 3 \ cm =144 \cdot \sqrt3^2 \ cm^3=144 \cdot 3 \ cm^3 \\ \Rightarrow \boxed{V=432 \ cm^2}$