In the given figure, ABCD is a square of side 5 cm inscribed in a circle. Find :

(i) the radius of the circle,

(ii) the area of the shaded region.

(i) Given,

Side of a square = 5 cm.

From figure,

Diagonal of square = Diameter of circle

Diagonal of square = $\sqrt{2}$ × Side of square

= $5\sqrt{2}$ cm

∴ Radius = $\dfrac{\text{Diameter}}{2} = \dfrac{5\sqrt{2}}{2}$ cm.

Hence, radius of circle = $\dfrac{5\sqrt{2}}{2}$ cm.

(ii) Area of shaded region = Area of circle - Area of square

$= 3.14 \times \Big(\dfrac{5\sqrt{2}}{2}\Big)^2 - 5^2 \\[1em] = 3.14 \times \dfrac{50}{4} - 25 \\[1em] = 3.14 \times \dfrac{25}{2} - 25 \\[1em] = 39.25 - 25 \\[1em] = 14.25 \text{ cm}^2.$

Hence area of shaded region = 14.25 cm².