The lengths of the diagonals of a rhombus are 24 cm and 18 cm respectively. Its area is

Options

A. `432cm^(2)`
B. `216cm^(2)`
C. `108cm^(2)`
D. `144cm^(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 \( d_1 = 24 \) cm (the length of the first diagonal).
- Given \( d_2 = 18 \) cm (the length of the second diagonal).

2. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \times 24 \times 18 \]

3. **Calculate half of the first diagonal**:
\[ \frac{1}{2} \times 24 = 12 \]

4. **Multiply this result by the second diagonal**:
\[ 12 \times 18 = 216 \]

5. **State the final area**:
\[ \text{Area of the rhombus} = 216 \text{ cm}^2 \]

### Final Answer:
The area of the rhombus is \( 216 \text{ cm}^2 \).