The the radius of the circle is given by the formula r=(3^(1/2)×a)/6.
Now the diameter of this circle would be the diagonal of the square.Which gives the side of the square as ((3/2)^(1/2)×a)/3
Therefor area of the square would be a^2.
It would be more helpful for you if you understood how the formula for radius of circle inscribed in an equilateral triangle.
Hope i was able to help.
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