If the circumference of a circle is equal to the perimeter of a square, and the radius of the given circle is positive, then which of the following options is correct?

Area of the circle > Area of the square

We know that,

Area of circle = πr²

Circumference of circle = 2πr

Perimeter of square = 4a

Area of square = a²

According to the question,

2πr = 4a

2 × \(\frac{22}{7}\) × r = 4a

\(\frac{44}{7}\) × r = 4a

\(\frac{r}{a}\) = \(\frac{7}{11}\)

Now the area of circle = πr² = \(\frac{22}{7}\) × 7 × 7 = 154

The area of square = a² = 11² = 121

So we can clearly see that Area of the circle > Area of the square