If the length of the diagonal AC of a square ABCD is 5.2 cm, then the area of the square is :

Options

A. 15.12 sq. cm
B. 13.52 sq. cm
C. 12.62 sq. cm
D. 10.00 sq. cm.

Answer

To find the area of the square ABCD when the length of the diagonal AC is given as 5.2 cm, we can follow these steps:

### Step 1: Understand the relationship between the diagonal and the side of the square.
The diagonal \( d \) of a square is related to its side length \( a \) by the formula:
\[ d = a \sqrt{2} \]

### Step 2: Substitute the given diagonal length into the formula.
Given that the diagonal \( d = 5.2 \) cm, we can substitute this value into the formula:
\[ 5.2 = a \sqrt{2} \]

### Step 3: Solve for the side length \( a \).
To find \( a \), we can rearrange the equation:
\[ a = \frac{5.2}{\sqrt{2}} \]

### Step 4: Calculate \( a \).
Now, we need to calculate \( a \):
\[ \sqrt{2} \approx 1.414 \]
Thus,
\[ a = \frac{5.2}{1.414} \approx 3.67 \text{ cm} \]

### Step 5: Calculate the area of the square.
The area \( A \) of the square is given by:
\[ A = a^2 \]
Substituting the value of \( a \):
\[ A = (3.67)^2 \approx 13.4689 \text{ cm}^2 \]

### Step 6: Round the area to two decimal places.
Rounding \( 13.4689 \) to two decimal places gives us:
\[ A \approx 13.47 \text{ cm}^2 \]

### Final Answer:
The area of the square ABCD is approximately \( 13.47 \text{ cm}^2 \).

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