If the circumference of a circle and the perimeter of a square are equal, then


We are given that


Circumference of a circle = Perimeter of square


Let r be the radius of the circle and a be the side of square.


from the given condition, we have 2π r = 4a


(22/7)r = 2a


11r = 7a


a = (11/7)a


r = (7/11)a …………..(i)


Now, area of circle = A1 = πr2 and area of square = A2 = a2


From equation (i ), we have


A1 = π × (7/11)2


= (22/7) × (49/121)a2


= (14/11)a2 and A2 = a2


A1 = (14/11) A2


A1 > A2


Hence, Area of the circle > Area of the square.

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