The area of a square with perimeter 40 cm is ________ .

Options

A. 1600 sq. cm
B. 10 sq. cm
C. 100 sq. cm
D. 250 sq. cm

Answer

To find the area of a square with a given perimeter of 40 cm, follow these steps:

### Step 1: Understand the relationship between perimeter and side length.
The perimeter (P) of a square is calculated using the formula:
\[ P = 4 \times \text{side length} \]
Let the side length of the square be \( x \).

### Step 2: Set up the equation for the perimeter.
Given that the perimeter is 40 cm, we can write:
\[ 4x = 40 \]

### Step 3: Solve for the side length \( x \).
To find \( x \), divide both sides of the equation by 4:
\[ x = \frac{40}{4} \]
\[ x = 10 \, \text{cm} \]

### Step 4: Calculate the area of the square.
The area (A) of a square is given by the formula:
\[ A = \text{side length} \times \text{side length} = x \times x = x^2 \]
Substituting the value of \( x \):
\[ A = 10 \times 10 = 100 \, \text{cm}^2 \]

### Step 5: State the final answer.
The area of the square with a perimeter of 40 cm is:
\[ \text{Area} = 100 \, \text{cm}^2 \]

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