The length of AB is [tex]\sqrt{\pi}[/tex]
Step-by-step explanation:
There is some missing information: I assume that AB is the side of square.
So in this problem we want to find the length of the side of the square.
We know the following information:
- The radius of the circle is r = 1
- The area of the circle is equal to the area of the square
The area of a circle is given by
[tex]A=\pi r^2[/tex]
where r is the radius.
The area of a square is given by
[tex]A=L^2[/tex]
where L is the length of the side.
Since here the area of the two figures is the same, we have
[tex]\pi r^2 = L^2[/tex]
And solving for L and substituting r = 1, we find the length of AB:
[tex]L=r\sqrt{\pi}=\sqrt{\pi}[/tex]
Learn more about area of a figure:
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