Answer
$52$ square kilometers.
Work Step by Step
Using that we have obtained the lengths of the sides: $s=0.5(a+b+c)=0.5(10+12+11)=16.5$
Then the area of the triangle is: $\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{16.5(16.5-10)(16.5-12)(16.5-11)}\approx52$ square kilometers.