The perimeter of any square is 420 cm, then the area of this square will

Question

Accepted Answer

To determine the area of a square given its perimeter, we need to follow these steps:

1. **Understanding the Perimeter of a Square:**
   - The perimeter of a square is calculated as 4 times the length of one side. If the perimeter is given as 420 cm, we can set up the equation:
     $$
     4 \times \text{side length} = 420 \text{ cm}
     $$

2. **Calculating the Side Length:**
   - Solving for the side length, we divide both sides of the equation by 4:
     $$
     \text{side length} = \frac{420 \text{ cm}}{4} = 105 \text{ cm}
     $$

3. **Calculating the Area of the Square:**
   - The area of a square is calculated as the side length squared. Therefore:
     $$
     \text{Area} = (\text{side length})^2 = (105 \text{ cm})^2 = 11025 \text{ cm}^2
     $$

4. **Justification for Option 3:**
   - The calculated area of the square is 11025 cm², which matches Option 3. Therefore, Option 3 is the correct answer.

5. **Explanation of Why Other Options Are Incorrect:**
   - **Option 1 (225 cm²):** This option is incorrect because it does not match the calculated area of 11025 cm². The value 225 cm² is significantly smaller than the correct area.
   - **Option 2 (225 cm):** This option is incorrect because it represents a linear measurement, not an area. The area of a square should be expressed in square units (cm²), not linear units (cm).
   - **Option 4 (11025 cm):** This option is incorrect because it also represents a linear measurement rather than an area. The correct area should be expressed in square units (cm²), not linear units (cm).

In conclusion, the correct answer is Option 3, 11025 cm², as it accurately represents the area of the square given the perimeter of 420 cm.