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.