Answer
$$r=\frac{\pm\sqrt{2A\theta}}{\theta}$$
Work Step by Step
To solve for r, isolate $r^2$ on one side of the equation
$A=\frac{1}{2}r^2\theta$
$(2)A=\frac{1}{2}(2)r^2\theta$
$2A=r^2\theta$
$\frac{2A}{\theta}=r^2$
apply the square root property: $x^2=k$, $x=\pm\sqrt{k}$
$r=\pm\sqrt{\frac{2A}{\theta}}$
$r=\pm\sqrt{\frac{2A}{\theta}\times\frac{\theta}{\theta}}$
$r=\pm\sqrt{\frac{2A\theta}{(\theta)^2}}$
$$r=\frac{\pm\sqrt{2A\theta}}{\theta}$$