The area of a rhombus if the lengths of whose diagonals are 16 cm and 24 cm, is

Options

A. 180 `cm^(2)`
B. 184 `cm^(2)`
C. 198 `cm^(2)`
D. 192 `cm^(2)`

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 \(d_1 = 16 \, \text{cm}\) and \(d_2 = 24 \, \text{cm}\).

2. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \times 16 \times 24 \]

3. **Calculate the product of the diagonals**:
- First, calculate \(16 \times 24\):
\[ 16 \times 24 = 384 \]

4. **Multiply by \(\frac{1}{2}\)**:
\[ \text{Area} = \frac{1}{2} \times 384 = 192 \, \text{cm}^2 \]

5. **Final Answer**:
- The area of the rhombus is \(192 \, \text{cm}^2\).