Answer
$382 \, in^2$
Work Step by Step
$s = \dfrac{1}{2}(a+b+c) = \dfrac{1}{2}(23+34+45) = 51 \, in$
$S = \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{51 (51-23)(51-34)(51-45)}$
$S = 382 \, in^2$
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