Answer
$\color{blue}A=\pi{x^2}$
Work Step by Step
$A$ varies directly with $x^2$, so the equation that represents the variation is:
$A=kx^2$
Since $A=4\pi$ when $x=2$ , substituting these into the tentative equation above gives:
$A=kx^2
\\4\pi=k(2^2)
\\4\pi=k(4)
\\\frac{4\pi}{4} = k
\\\pi=k$
Thus, the equation of the direct variation is:
$\color{blue}A=\pi{x^2}$