The side of a square is 10 cm.

It is given that the side of square is 10 cm.

So, the diameter of circle inscribed the square is 10 cm.

We know that the area A of circle inscribed the square is

$A=\pi r^{2}$

Substituting the value of radius of inscribed circle $r=5 \mathrm{~cm}$,

$A=3.14 \times 5 \times 5$

$=78.5 \mathrm{~cm}^{2}$

Hence the area of circle inscribed the square is $78.5 \mathrm{~cm}^{2}$

Now we will find the diameter of circle circumscribed the square.

diameter of circle circumscribed the square = diameter of square

$=\sqrt{(10)^{2}+(10)^{2}}$

$=10 \sqrt{2} \mathrm{~cm}$

So, radius of circle circumscribed the square $=5 \sqrt{2} \mathrm{~cm}$

We know that the area  of circle inscribed the square is

$A^{\prime}=\pi r^{\prime 2}$

Substituting the value of radius,

$A^{\prime}=3.14 \times 5 \sqrt{2} \times 5 \sqrt{2}$

$=157 \mathrm{~cm}^{2}$

Hence the area of circle circumscribed the square is $157 \mathrm{~cm}^{2}$.