Răspuns:
SA=36[tex]\sqrt{6}[/tex]
Explicație pas cu pas:
ABC echilateral=> SABC piramida triunghiulara regulata=>
SA=SB=SC
ΔSAC=ΔSBC=ΔSAB
ΔSAB(∡A=90°)
[tex]AS^{2}[/tex]+[tex]SB^{2}[/tex]=[tex]AB^{2}[/tex] , AS=SB
2 [tex]SA^{2}[/tex] = [tex]AB^{2}[/tex]
[tex]SA^{2}[/tex]=[tex]AB^{2}[/tex]/2
SA=AB/[tex]\sqrt{2}[/tex]
SA=72[tex]\sqrt{3}[/tex]/[tex]\sqrt{2}[/tex] , rationalizam
SA=36[tex]\sqrt{6}[/tex]
