[tex]Heron's\ formula:\\A_\Delta=s\sqrt{(s-a)(s-b)(s-c)}\ where\ s=\dfrac{a+b+c}{2}\\\\a=5;\ b=8;\ c=11\\\\s=\dfrac{5+8+11}{2}=\dfrac{24}{2}=12\\\\A_\Delta=12\sqrt{(12-5)(12-8)(12-11)}=12\sqrt{7\cdot4\cdot1}\\\\=12\sqrt7\cdot\sqrt4=12\sqrt7\cdot2=24\sqrt7[/tex]
