Question

Prisma triunghiulara regulata dreapta ABCA'B'C' are aria totala de 162√3cm^ si aria laterala de 108√3cm^ Aflati:
a) Latura bazei si Inaltimea prismei
b) Volumul prismei

Answer 1

[tex]a)A_t=A_l+2\cdot A_b\\ 162\sqrt3=108\sqrt3+2\cdot A_b\\ 2\cdot A_b= 54 \sqrt3\\ A_b=27\sqrt3 \\ \frac{l^2\sqrt3}{4}=27\sqrt3\\ l^2=108 \Rightarrow l=6\sqrt3 cm\\ A_l=P_b\cdot h\\ 108\sqrt3=18\sqrt3\cdot h\\ h=6\ cm\\ b)V=A_b\cdot h\\ V=27\sqrt3\cdot 6\\ V=162\sqrt 3\ cm^3 [/tex]