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

Options

A. `225 cm^(2)`
B. 225 cm
C. `11025 cm^(2)`
D. 11025 cm

Answer

To find the area of a square when the perimeter is given, we can follow these steps:

### Step 1: Understand the formula for the perimeter of a square.
The perimeter (P) of a square is given by the formula:
\[ P = 4 \times \text{side} \]

### Step 2: Set up the equation using the given perimeter.
Given that the perimeter of the square is 420 cm, we can write:
\[ 4 \times \text{side} = 420 \]

### Step 3: Solve for the side length of the square.
To find the side length, divide both sides of the equation by 4:
\[ \text{side} = \frac{420}{4} \]
\[ \text{side} = 105 \, \text{cm} \]

### Step 4: Use the side length to find the area of the square.
The area (A) of a square is given by the formula:
\[ A = \text{side}^2 \]
Substituting the value of the side we found:
\[ A = 105^2 \]

### Step 5: Calculate the area.
Now, calculate \( 105 \times 105 \):
\[ A = 11025 \, \text{cm}^2 \]

### Final Answer:
The area of the square is \( 11025 \, \text{cm}^2 \).

---