Perimeter of a square is equal to circumference of a circle. If area of square is 12100 square meters, then area of circle is equal to :

Question

Accepted Answer

To determine why Option 4 is the correct answer, let's go through the problem step by step:

1. **Understanding the Problem:**
   - We are given that the perimeter of a square is equal to the circumference of a circle.
   - The area of the square is 12100 square meters.

2. **Calculating the Side of the Square:**
   - The area of a square is given by the formula: Area = side².
   - Therefore, side² = 12100.
   - Solving for the side, we get side = √12100 = 110 meters.

3. **Calculating the Perimeter of the Square:**
   - The perimeter of a square is given by the formula: Perimeter = 4 × side.
   - Therefore, Perimeter = 4 × 110 = 440 meters.

4. **Relating the Perimeter to the Circumference of the Circle:**
   - We know that the perimeter of the square (440 meters) is equal to the circumference of the circle.
   - The formula for the circumference of a circle is: Circumference = 2πr, where r is the radius.
   - Therefore, 2πr = 440.
   - Solving for r, we get r = 440 / (2π) = 220 / π meters.

5. **Calculating the Area of the Circle:**
   - The area of a circle is given by the formula: Area = πr².
   - Substituting the value of r, we get Area = π(220/π)² = (220²)/π square meters.
   - Calculating this gives Area ≈ 15400 square meters.

6. **Conclusion:**
   - The calculated area of the circle is approximately 15400 square meters, which matches Option 4.

**Explanation of Incorrect Options:**

- **Option 1 (440 square meters):** This value is incorrect because it represents the perimeter of the square and the circumference of the circle, not the area of the circle.
  
- **Option 2 (14000 square meters):** This value is incorrect because it does not match the calculated area of the circle, which is approximately 15400 square meters.

- **Option 3 (15200 square meters):** This value is also incorrect because it is close but does not match the precise calculation of the circle's area, which is approximately 15400 square meters.

Therefore, based on the calculations and logical reasoning, Option 4 (15400 square meters) is indeed the correct answer.