Question

Fie VABC o piramida triunghiulara regulata cu varful in V care are aria bazei de 4 radical din 3 cm^2 si aria unei fete laterale de 8 radical din 3 cm^2.Aflati a) l b) Pb c)m d) Pf

Answer 1

Ab=l²√3/4<=>4√3=l²√3/4<=>4=l²/4=>l²=16=>l=√16=>l=4 cm

Pb=3*l=3*4=12 cm

Al=3*A=3*8√3 =24√3 cm²

Al=Pb*a/2<=>24√3 =12a/2<=>24√3 =6a=>a=4√3 cm

m²=(l/2)²+a²=(4/2)²+(4√3)²=2²+16*3=4+48=52=>m=√52=2√13 cm

Pf=3*(2m+l)=3(4√13+4) cm