SOLUTION
Since the circle is inscribe in the square, the lenght of the square will in turn be the diameter of the circle.
[tex]\begin{gathered} \text{length of square =diameter of circle} \\ l=d \\ 12in=d \\ \text{Therefore diameter of the circle is 12 inches.} \\ \end{gathered}[/tex]The area of a circle is calculated with the formula:
[tex]\pi r^2[/tex][tex]\begin{gathered} r=\frac{d}{2} \\ r=\frac{12}{2} \\ r=6in \end{gathered}[/tex]Substitute this value into the formula for area of a circle:
[tex]\begin{gathered} \pi r^2 \\ 3.14\times6^2 \\ 3.14\times36 \\ 113.04in^2 \end{gathered}[/tex]The area of the inscribed circle is 113.04 square inches.