Help needed in understanding Heron's Formula So i just started learning Trigonometry seriously and something doesn't feel right to me, either I'm missing something or not but.
Lets assume we have a triangle

and there are two ways to find the area.
1 is using the standard $$A = \frac{1}{2}bh$$ and by using the example image above we get $A = 10625$
but if I use the other formula, in this case, Heron's Formula 
\begin{align*}
s & = \frac{a+b+c}{2}\\
A & = \sqrt{s(s-a)(s-b)(s-c)}
\end{align*}
the area becomes $A = 10620.09$.
They're both gravely close to each other, which has me thinking maybe I missed something.
So my question is, why are the areas different?

You shouldn't consider the areas different, because the relative difference is smaller than $0.05\%$.
But you can a priori expect an error on the height to be up to $0.5\%$ as some number is truncated to integer. Hence without deeper error calculus, you can't be conclusive.
