Area of a triangle with Heron's formula

Text

A triangle has sides $17$, $25$ and $28$. Using Heron’s formula $A=\sqrt{s(s-a)(s-b)(s-c)}$, with $s$ the semiperimeter, compute its area.

Solution

The semiperimeter is $s=\frac{17+25+28}{2}=35.$ Therefore $A=\sqrt{35\,(35-17)(35-25)(35-28)}=\sqrt{35\cdot 18\cdot 10\cdot 7}=\sqrt{44100}=\boxed{210}.$