Let a be the side of square.

∴ Diameter of a circle = Diagonal of the square = 8 cm

Now in right angled triangle ABC,

(AC)² = (AB)² + (BC)²

(By Pythagoras theorem)

∴ (8)²= a² +a²

⇒ 64= 2a²

⇒ a²= 32

Hence area of square = a²= 32 cm²

∴ Radius of the circle = Diameter/2 = 4 cm

∴ Area of the circle = πr² = π(4)² = 16 cm²

So, the area of the shaded region = Area of circle – Area of square

∴ the area of the shaded region = 16π – 32

= 16 × (22/7) – 32

= 128/7

= 18.286 cm²