The perimeter of a square is 22 cm. Find its area (in `cm^(2)`).

Options

A. `60.5`
B. `22.5`
C. 45
D. `30.25`

Answer

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

### Step-by-Step Solution:

1. **Understand the relationship between perimeter and side length 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.

2. **Set up the equation using the given perimeter**:
We know the perimeter is 22 cm, so we can set up the equation:
\[ 4 \times \text{side} = 22 \]

3. **Solve for the side length**:
To find the side length, divide both sides of the equation by 4:
\[ \text{side} = \frac{22}{4} = 5.5 \text{ cm} \]

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 side length we found:
\[ A = 5.5 \times 5.5 = 30.25 \text{ cm}^2 \]

5. **Final answer**:
Therefore, the area of the square is:
\[ \text{Area} = 30.25 \text{ cm}^2 \]