The side of a square is 10 cm.

Solution:

(​i)​ If a circle is inscribed in a square, then the side of the square is equal to the diameter of the circle.
Side of the square = 10 cm
Side = Diameter = 10
∴ Radius = 5 cm

Area of the inscribed circle $=\pi r^{2}$

$=3.14 \times 5 \times 5$

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

(ii) If a circle is circumscribed in a square, then the diagonal of the square is equal to the diameter of the circle.

Diagonal of the square $=\sqrt{2} \times$ Side of the square

$=\sqrt{2} \times 10$

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

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

$\therefore r=5 \sqrt{2} \mathrm{~cm}$

Now,

Area of the circumscribed circle $=\pi r^{2}$

$=3.14 \times(5 \sqrt{2})^{2}$

$=3.14 \times 50$

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