If the length of a square is `(a + b)` then the area of the square will be :

Options

A. `(a+b)^(2)`
B. `1/2(a + b)^(2)`
C. `(a^(2)+ b^(2))`
D. `1/2(a^(2) + b^(2))`

Explanation

To solve the problem, we need to find the area of a square when the length of each side is given as \( (a + b) \).

### Step-by-Step Solution:

1. **Identify the length of the side of the square**:
The problem states that the length of the square is \( (a + b) \). This means that each side of the square measures \( (a + b) \).

**Hint**: Remember that all sides of a square are equal.

2. **Recall the formula for the area of a square**:
The area \( A \) of a square is calculated using the formula:
\[ A = \text{side}^2 \]

**Hint**: The area is always the side length multiplied by itself.

3. **Substitute the length of the side into the area formula**:
Since the side of the square is \( (a + b) \), we substitute this into the area formula:
\[ A = (a + b)^2 \]

**Hint**: When substituting, ensure you square the entire expression.

4. **Expand the expression** (if required):
The expression \( (a + b)^2 \) can be expanded using the formula \( (x + y)^2 = x^2 + 2xy + y^2 \):
\[ A = a^2 + 2ab + b^2 \]
However, the question asks for the area in terms of \( (a + b) \), so we can leave it as \( (a + b)^2 \).

**Hint**: Expanding is optional unless specifically asked for the expanded form.

5. **Conclusion**:
Therefore, the area of the square is:
\[ A = (a + b)^2 \]

### Final Answer:
The area of the square is \( (a + b)^2 \).