A circular field and a square field have the same perimeter. If the area of the square field is 12,100 m², what is the area of the circular field?

Explanation

Given that the square field has an area of 12,100 m², the side length is √12100 = 110 m. The perimeter of the square is 4 × 110 = 440 m, which equals the circumference of the circle. Using the formula for circumference, 2πr = 440, we find the radius r = 440 / (2π) ≈ 70 m. The area of the circle is πr² ≈ 3.14 × 70² = 15,400 m².