In figure, a square of diagonal 8 cm is inscribed in a circle. Find the area of the shaded region.


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


2
1