Triangle with sides a,b,c and area There is a triangle with sides $a,b,c$, then his area is: 
a) $A$ not greater than $\frac{1}{2}(a^2-ab+b^2)$
b) $B$ greater than $\frac{1}{2}(a^2-ab+b^2)$
c) $C$ greater than $\frac{1}{2}(a^2-\frac{1}{2}ab+b^2)$
d) $D$ less than $\frac{1}{2}(a^2+ab+b^2)$
I am thinking about applying the Heron formula here, because we know all its sides. 

HINT:
The area is $\displaystyle\triangle= \frac12ab\sin\gamma$
As $\displaystyle 0<\sin\gamma\le1, ab\sin\gamma\le ab\iff -ab\sin\gamma\ge -ab$
$\displaystyle\implies A-\triangle=\frac{a^2-ab+b^2-ab\sin\gamma}2\ge\frac{a^2-ab+b^2-ab}2$ which is $\displaystyle\frac{(a-b)^2}2\ge0$
