What is the area of a square having perimeter 68 cm?

Options

A. 361 sq cm
B. 284 sq cm
C. 269 sq cm
D. 289 sq cm

Answer

To find the area of a square 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 calculated using the formula:
\[ P = 4 \times \text{side} \]
where "side" is the length of one side of the square.

### Step 2: Set up the equation using the given perimeter
We know the perimeter is 68 cm, so we can set up the equation:
\[ 4 \times \text{side} = 68 \]

### Step 3: Solve for the side length
To find the length of one side, we divide both sides of the equation by 4:
\[ \text{side} = \frac{68}{4} \]
\[ \text{side} = 17 \text{ cm} \]

### Step 4: Calculate the area of the square
The area (A) of a square is given by the formula:
\[ A = \text{side}^2 \]
Now, substituting the value of the side we found:
\[ A = 17^2 \]
\[ A = 17 \times 17 \]
\[ A = 289 \text{ cm}^2 \]

### Conclusion
The area of the square is \( 289 \text{ cm}^2 \).

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