FORMULA LUI HERRON:
[tex] A_{triunghiului}=\sqrt{p(p-a)(p-b)(p-c)}[/tex]
p-semiperimetrul triunghiului
a,b,c-lungimile laturilor triunghiului
[tex] p_{\deltaABC}=\frac{AB+BC+AC}{2}=\frac{6cm+9cm+11cm}{2}=\frac{26cm}{2}=13cm[/tex]
[tex] A_{[ABC]}=\sqrt{13(13-6)(13-9)(13-11)}[/tex]
[tex] A_{[ABC]}=\sqrt{13*7*4*2}[/tex]
[tex] A_{[ABC]}=\sqrt{728}[/tex]
[tex]728=2^{3}*13*7[/tex]
=> [tex] A_{[ABC]}=\sqrt{2^{2}*182}[/tex]
=> [tex] A_{[ABC]}=2\sqrt{182}cm^{2}[/tex]
