Question

o prisma triunghiulara regulata dreapta ABCA'B'C' AB=2 m si AA'=8m Calculati aria laterala ,aria totala si volumul

Answer 1

   
[tex]\texttt{Se da: } \\ \texttt{Latura bazei }=l= AB = 2~m \\ \texttt{Inaltimea prismei }=h_p= AA' = 8~m \\ \texttt{Se cere: } \\ Al = ? \\ At = ? \\ V = ? \\ \texttt{Calculam valori intermediare: } \\ \text{Inaltimea triunghiului echilateral al bazei: } \\ h_t = \frac{l \sqrt{3} }{2} =\frac{2 \sqrt{3} }{2} = \sqrt{3}~m\\ \text{Perimetrul bazei: } \\ P = 3l = 3 \times 2 = 6~m \\ \text{Aria bazei: } \\ Ab = \frac{l \times h_t}{2}= \frac{2 \times \sqrt{3}}{2}= \sqrt{3}~m^2 [/tex]


[tex]\texttt{Rezolvare: } \\ Al = P \times h_p = 6 \times 8 = \boxed{48~m^2} \\ \\ At = Al + 2Ab = \boxed{(48 + 2 \sqrt{3} ) ~m^2} \\ \\ V = Ab \times h_p = \sqrt{3} \times 8 = \boxed{8\sqrt{3}~m^3}[/tex]