Answer
$18 \text{ square units}$
Work Step by Step
Let the side of the square be $a$.
The diagonal divides the square into two congruent right triangles, with the base and height equal to $a$.
The diagonal of the square is the diameter of the circle.
Using the standard form $x^2+y^2=r^2$ (where $r$ is the radius) as basis, the value of $r$ is $\sqrt9=3$.
Hence, the diameter of the circle is $2\times3=6$.
Thus, the hypotenuse of the right triangle is $6$ units.
The area of a square is equal to the square of its side.
Using Pythagorean Theorem givesx_{y}:
\begin{align*}
\text{(base)}^2 + \text{(height)}² &= \text{(hypotenuse)}^2\\
a^2 + a^2 &= 6^2\\.
2a^2 &= 36\\
a^2 = 18\\
\end{align*}
Therefore, the area of the square is $18 \text{ square units}$.
