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

Let the length of the side of the square be a

Let the radius if circle be r

Perimeter of circle = 2πr

Perimeter of square = 4a

Perimeter of circle = Perimeter of square

2πr = 4a

a = π × r/2

Area of a square = a^{2}

= (π × r/2)^{2} = π/4 × πr^{2}

Area of circle = πr^{2}

Seeing the co-efficient of πr^{2}

1 > π/4 ∴ πr^{2} > π/4 × πr^{2}

So, (area of the circle) > (area of the square)

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