Explicație pas cu pas:
Folosim formula lui Heron:
Afla semiperimetrul:
p=(7+25+24)/2=28(cm)
A=√[28(28-7)(28-25)(28-24)]=√[28*21*3*4]=√[7056]=
=84(cm²)
Bafta!
[tex]\displaystyle\bf\\\text{Se da:}\\\Delta ABC\text{~\bf cu }AB=7~cm;~BC=25~cm;~AC=24~cm\\\\\text{Se cere:}\\a)~~Aria~\Delta ABC\\\\\text{\bf~Rezolvare:}\\\\\text{\bf Folosim formula lui Heron.}\\\\Aria~\Delta ABC=\sqrt{p(p-AB)(p-BC)(p-AC)}\\p=semiperimetrul~triunghiului\\P=AB+BC+AC=7+25+24=56~cm\\\\p=\frac{P}{2}=\frac{56}{2}=28~cm[/tex]
[tex]\displaystyle\bf\\Aria~\Delta ABC=\sqrt{28(28-7)(28-25)(28-24)}=\\\\=\sqrt{28\times21\times3\times4}=\\\\=\sqrt{4\cdot7\times3\cdot7\times3\times4}=\\\\=\sqrt{4^2\times7^2\times3^2}=\\\\=4\times7\times3=84~cm^2\\\\\boxed{\bf~Aria~\Delta ABC=84~cm^2}[/tex]
