What would be the area fo a square whose diaonal measures 28 cm?

Options

A. 288 sq cm
B. 214 sq cm
C. 428 sq cm
D. 392 sq cm

Explanation

To find the area of a square when the diagonal is given, we can follow these steps:

### Step 1: Understand the relationship between the diagonal and the area of the square.
The area \( A \) of a square can be calculated using the formula:
\[ A = \frac{1}{2} \times d^2 \]
where \( d \) is the length of the diagonal.

### Step 2: Substitute the given diagonal length into the formula.
In this case, the diagonal \( d \) is given as 28 cm. We substitute this value into the formula:
\[ A = \frac{1}{2} \times (28)^2 \]

### Step 3: Calculate the square of the diagonal.
First, we calculate \( 28^2 \):
\[ 28^2 = 784 \]

### Step 4: Calculate the area using the diagonal squared.
Now, substitute \( 784 \) back into the area formula:
\[ A = \frac{1}{2} \times 784 \]

### Step 5: Perform the division.
Now, we divide \( 784 \) by \( 2 \):
\[ A = 392 \text{ cm}^2 \]

### Conclusion:
The area of the square whose diagonal measures 28 cm is \( 392 \text{ cm}^2 \).

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