Find the area of a square whose perimeter is 84 cm.

Options

A. `21cm^2`
B. `441 cm^2`
C. `7056 cm^2`
D. None of these

Answer

To find the area of a square whose perimeter is 84 cm, 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:
\[ P = 4 \times \text{side} \]
where "side" is the length of one side of the square.

### Step 2: Set up the equation using the given perimeter.
Since the perimeter is given as 84 cm, we can set up the equation:
\[ 4 \times \text{side} = 84 \]

### Step 3: Solve for the length of one side.
To find the length of one side, divide both sides of the equation by 4:
\[ \text{side} = \frac{84}{4} \]
\[ \text{side} = 21 \text{ cm} \]

### Step 4: Calculate the area of the square.
The area (A) of a square is given by the formula:
\[ A = \text{side} \times \text{side} \]
Substituting the value of the side we found:
\[ A = 21 \times 21 \]

### Step 5: Perform the multiplication.
Calculating \( 21 \times 21 \):
\[ A = 441 \text{ cm}^2 \]

### Final Answer:
The area of the square is \( 441 \text{ cm}^2 \).

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