The lengths of two diagonals of a rhombus are 10 cm and 24 cm. What is the area (in `cm^(2)`) of the rhombus?

Options

A. 60
B. 90
C. 120
D. 240

Answer

To find the area of a rhombus given the lengths of its diagonals, 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 \(d_1 = 10 \, \text{cm}\) and \(d_2 = 24 \, \text{cm}\).

2. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \times 10 \times 24 \]

3. **Calculate the product of the diagonals**:
\[ 10 \times 24 = 240 \]

4. **Multiply by \(\frac{1}{2}\)**:
\[ \text{Area} = \frac{1}{2} \times 240 = 120 \, \text{cm}^2 \]

5. **Conclusion**:
The area of the rhombus is \(120 \, \text{cm}^2\).