Given:
The largest possible circle is cut out of a square whose side lenght is 12 feet.
The area of square is given by,
[tex]\begin{gathered} A=(side)^2 \\ A=12^2=144 \end{gathered}[/tex]
The radius of circle will be,
[tex]r=\frac{12}{2}=6\text{ f}eet[/tex]
And the area of circle is ,
[tex]\begin{gathered} A=\pi(r)^2 \\ A=\pi(6)^2 \\ A=36\pi \end{gathered}[/tex]
The area left when circle is cut out of a square is ,
[tex]\begin{gathered} \text{Area left = 144- 36}\pi \\ =30.9\text{ }\approx31\text{ square f}eet \end{gathered}[/tex]
Hence, the required area is 31 square feet.
