The side of a square is 10 cm.

Solution:

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