Find the area and the perimeter of a square with diagonal 24 cm.
[Take `sqrt(2)=1.41`].

Answer

To find the area and the perimeter of a square with a diagonal of 24 cm, we can follow these steps:

### Step 1: Understand the relationship between the diagonal and the side of the square
In a square, if 'a' is the length of a side, the diagonal 'd' can be calculated using the Pythagorean theorem:
\[ d = a\sqrt{2} \]

### Step 2: Set up the equation
Given that the diagonal \( d = 24 \) cm, we can set up the equation:
\[ 24 = a\sqrt{2} \]

### Step 3: Solve for 'a'
To find 'a', we can rearrange the equation:
\[ a = \frac{24}{\sqrt{2}} \]

### Step 4: Substitute the value of \( \sqrt{2} \)
Using the given value \( \sqrt{2} = 1.41 \):
\[ a = \frac{24}{1.41} \]

### Step 5: Calculate the value of 'a'
Calculating this gives:
\[ a \approx 17.02 \text{ cm} \]

### Step 6: Calculate the area of the square
The area \( A \) of a square is given by:
\[ A = a^2 \]
Substituting the value of 'a':
\[ A = (17.02)^2 \]
Calculating this gives:
\[ A \approx 289.68 \text{ cm}^2 \]

### Step 7: Calculate the perimeter of the square
The perimeter \( P \) of a square is given by:
\[ P = 4a \]
Substituting the value of 'a':
\[ P = 4 \times 17.02 \]
Calculating this gives:
\[ P \approx 68.08 \text{ cm} \]

### Final Results
- Area of the square: \( 289.68 \text{ cm}^2 \)
- Perimeter of the square: \( 68.08 \text{ cm} \)

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