Answer
The area of Arizona is $111,416 mi^{2}$
Work Step by Step
Typical percentage problem:
What percent ($n$, as a decimal number) of (the base amount $y)$ is $x?$
Translated:$\quad n\cdot y=x$
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Here, reworded, $\quad 19\%$ of ($y=586,400$) is ($x=?$).
Translated:$\quad 0.19\cdot 586,400=x$
($ 19\%$ converted to decimal notation is $0.19)$
$x=111,416 mi^{2}$
The area of Arizona is $111,416 mi^{2}$