The perimeter of a square is 26 cm. Find its area (in `cm^(2)`).

Options

A. `42.25`
B. `84.5`
C. `39.25`
D. `78.5`

Answer

To find the area of a square given its perimeter, 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:
\[ P = 4 \times \text{side} \]

### Step 2: Use the given perimeter to find the length of one side.
We know the perimeter is 26 cm. We can set up the equation:
\[ 4 \times \text{side} = 26 \]

### Step 3: Solve for the side length.
To find the length of one side, divide the perimeter by 4:
\[ \text{side} = \frac{26}{4} = 6.5 \text{ cm} \]

### Step 4: Calculate the area of the square.
The area \( A \) of a square is given by the formula:
\[ A = \text{side}^2 \]
Now, substitute the side length into the formula:
\[ A = (6.5)^2 \]

### Step 5: Perform the calculation.
Calculating \( (6.5)^2 \):
\[ A = 6.5 \times 6.5 = 42.25 \text{ cm}^2 \]

### Final Answer:
The area of the square is \( 42.25 \text{ cm}^2 \).

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