The perimeter of a square is numerically equal to its area. Find its area.

Answer

To solve the problem where the perimeter of a square is numerically equal to its area, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formulas**:
- The perimeter \( P \) of a square with side length \( a \) is given by:
\[ P = 4a \]
- The area \( A \) of a square is given by:
\[ A = a^2 \]

2. **Set up the equation**:
- According to the problem, the perimeter is equal to the area:
\[ 4a = a^2 \]

3. **Rearrange the equation**:
- Rearranging the equation gives:
\[ a^2 - 4a = 0 \]

4. **Factor the equation**:
- Factoring out \( a \) from the equation:
\[ a(a - 4) = 0 \]

5. **Find the possible values for \( a \)**:
- Setting each factor to zero gives us:
\[ a = 0 \quad \text{or} \quad a = 4 \]

6. **Evaluate the possible values**:
- The value \( a = 0 \) is not valid for the side of a square, so we take:
\[ a = 4 \]

7. **Calculate the area**:
- Now, substituting \( a = 4 \) into the area formula:
\[ A = a^2 = 4^2 = 16 \]

8. **Final answer**:
- Therefore, the area of the square is:
\[ \text{Area} = 16 \text{ square units} \]