If the circumference of a circle is equal to the perimeter of square, then which one of the following is correct? 

Formula used:

1. Area of circle = πr²

2. Circumference of circle = 2πr

3. Perimeter of square = 4a

4. Area of square = a²

Where, 

r = radius of circle and 

a = side of the square 

Calculation:

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

Then the area of a circle

A= πr² = 3.14 r²       ------(1)

According to the question, 

Circumference of a circle = perimeter of the square

⇒ 2πr = 4a

⇒ a = πr/2  

Hence the area of square

 \(a^2\ =\ (\frac{π r}{2})^2\) 

\(\Rightarrow \ a^2\ =\ 2.46\ r^2\)        -----(2)

From the equation (1) and (2), we can say that, Area of circle > Area of the square.