Area of the circle =[tex]\frac{x^2}{4\pi } \; square \; inches[/tex]
Area of square = [tex]\frac{x^2}{16}[/tex] square inches
Given :
A piece of wire that is x inches long . It is bent into shape of a circle
Perimeter of circle = x inches
we know that , perimeter of circle =[tex]2\pi r[/tex]
[tex]2\pi r=x\\solve \; for \; r\\divide \; both \; sides \; by \; 2\pi \\r=\frac{x}{2\pi } \\r=\frac{x}{2\pi }[/tex]
Now we find area of the circle using the radius
[tex]Area =\pi r^2\\Area=\pi (\frac{x}{2\pi } )^2\\Area=\pi (\frac{x^2}{4\pi ^2} )\\\\Area=\frac{x^2}{4\pi }[/tex]
Area of the circle =[tex]\frac{x^2}{4\pi } \; square \; inches[/tex]
Perimeter of square = 4(side)= 4s
4s=x
Divide both sides by 4
[tex]s=\frac{x}{4}[/tex]
Area of square =[tex]s^2=\frac{x}{4} ^2=\frac{x^2}{16}[/tex]
Area of square = [tex]\frac{x^2}{16}[/tex]
Learn more : brainly.com/question/4450298
