Answer
$3.8$ square feet.
Work Step by Step
Using that we have obtained the lengths of the sides: $s=0.5(a+b+c)=0.5(2.3+3.4+4.5)=5.1$
Then the area of the triangle is: $\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{5.1(5.1-4.5)(5.1-3.4)(5.1-2.3)}\approx3.8$ square feet.