Find the area of the rhombus , the lengths of whose diagonals are 17.5 cm and 22.4 cm.

Answer

To find the area of a rhombus when the lengths of its diagonals are given, we can use the formula:

\[ \text{Area} = \frac{1}{2} \times D_1 \times D_2 \]

where \( D_1 \) and \( D_2 \) are the lengths of the diagonals.

### Step-by-Step Solution:

1. **Identify the lengths of the diagonals**:
- Given \( D_1 = 17.5 \) cm and \( D_2 = 22.4 \) cm.

2. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \times D_1 \times D_2 = \frac{1}{2} \times 17.5 \times 22.4 \]

3. **Calculate the product of the diagonals**:
- First, calculate \( 17.5 \times 22.4 \):
\[ 17.5 \times 22.4 = 392 \]

4. **Divide by 2 to find the area**:
\[ \text{Area} = \frac{392}{2} = 196 \text{ cm}^2 \]

5. **State the final answer**:
- The area of the rhombus is \( 196 \text{ cm}^2 \).