#### Answer

$A=\pi r^2$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given formula, $
r=\sqrt{\dfrac{A}{\pi}}
$ for $
A
,$ square both sides and then use cross-multiplication to isolate the needed variable.
$\bf{\text{Solution Details:}}$
Squaring both sides of the given formula results to
\begin{array}{l}\require{cancel}
(r)^2=\left( \sqrt{\dfrac{A}{\pi}} \right)^2
\\\\
r^2=\dfrac{A}{\pi}
.\end{array}
Since $\dfrac{a}{b}=\dfrac{c}{d}$ implies $ad=bc$ or sometimes referred to as cross-multiplication, the equation above is equivalent to
\begin{array}{l}\require{cancel}
r^2(\pi)=1(A)
\\\\
\pi r^2=A
\\\\
A=\pi r^2
.\end{array}