The minimum possible area of the square cardboard will be given as
[tex]a= 72.2\ in ^2[/tex]
The area of the square is the product of its two lengths.
We have an equation of the circular drink coaster
[tex]x^2+y^2=18.0625[/tex]
Comparing the above equation from the general form of the circle
[tex]x^2+y^2=r^2[/tex]
We can see that from the equation
[tex]r^2=18.0625[/tex]
[tex]r=4.25\ inch[/tex]
Diameter [tex]d=4.25\times 2=8.50[/tex]
The diameter will be the length of the square since the circle is cut from the square.
So the area of the square will be
[tex]a=d\times d=8.50\times 8.50=72.25\ inch^2[/tex]
Thus the minimum possible area of the square cardboard will be given as [tex]a= 72.2\ in ^2[/tex]
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