Inscribed Things

I am assuming that it is the sizes of the areas of the two shapes are to be compared.

If the blue square has a side 2, then the green circle inscribed in it has a diameter 2.

The orange square is then inscribed in a circle with diameter 2.

So it is the orange square and the green circle we are comparing.

It is obvious that the orange square is smaller than the green circle within which it resides.

For the inscribed square

The diameter of the circle is $2$ . So, the diagonal of the square is, also, $2$ .
But, if $x$ is the side length of the square, then the diagonal, by Pythagorean Theorem, is $\sqrt{2}x$ . Thus we got:
$\sqrt{2}x=2\Rightarrow x=\frac{2}{\sqrt{2}}\Rightarrow x=\sqrt{2}$
So, the area of the square is: $(\sqrt{2})^{2}=2$

For the inscribed circle

The side length of the square is $2$ . So, the diameter of the circle is, also, $2$ .
Thus, the radius of the circle is $1$ and it's area is: $πr^{2}=π$

Conclusion

$π>2\Rightarrow$ Area of circle $>$ Area of square

just placing square on circle ...Square diameter =2 and Circle diameter is = 2.....but when you place square on circle, it gets fit in circle and circle has some area not covered by square!!