Big triangle

This is a direct application of the Herons formula. If $a,b,c$ are the sides of a triangle, then the area of the triangle is $\sqrt{s(s-a)(s-b)(s-c)}$ where $s=\frac{a+b+c}{2}$ is the semiperimeter.

Since $a=13, b=14, c=15$ , we have $s=\frac{13+14+15}{2}=21$ .

Substituting the respective values for $a,b,c$ and $s,$

$[ABC]=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{21(21-13)(21-14)(21-15)}=\sqrt{21\cdot 8\cdot 7\cdot 6}=\sqrt{7056}=84.$

Therefore the area of the triangle with side lengths 13, 14,15 is $\boxed{84}$