If the perimeter of a square is `(4a + 8) `unit, then its area will be

Options

A. `(a^2 + 4 a + 4)` sq unit
B. `(10 a^2 - a - 8)` sq unit
C. `(a + 2a^2 + 4)` sq unit
D. `(4a^2 + 4a - 4)` sq unit

Answer

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

### Step 1: Understand the relationship between perimeter and side length
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 for the given perimeter
We are given that the perimeter of the square is \( 4a + 8 \) units. Therefore, we can set up the equation:
\[ 4 \times \text{side} = 4a + 8 \]

### Step 3: Solve for the side length
To find the side length, we divide both sides of the equation by 4:
\[ \text{side} = \frac{4a + 8}{4} \]
Now, simplify the right side:
\[ \text{side} = a + 2 \]

### Step 4: Calculate the area of the square
The area \( A \) of a square is given by the formula:
\[ A = \text{side}^2 \]
Substituting the expression we found for the side:
\[ A = (a + 2)^2 \]

### Step 5: Expand the expression for the area
Now, we need to expand \( (a + 2)^2 \):
\[ A = (a + 2)(a + 2) = a^2 + 2a + 2a + 4 = a^2 + 4a + 4 \]

### Conclusion
Thus, the area of the square is:
\[ A = a^2 + 4a + 4 \text{ square units} \]