The diagonals of a rhombus are respectively 6 cm and 10 cm. What is the area (in `cm^(2)`)?

Options

A. 15
B. 30
C. 20
D. 60

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: \(d_1 = 6 \, \text{cm}\) (one diagonal)
- Given: \(d_2 = 10 \, \text{cm}\) (the other diagonal)

2. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \times 6 \times 10 \]

3. **Calculate the product of the diagonals**:
\[ 6 \times 10 = 60 \]

4. **Multiply by \(\frac{1}{2}\)**:
\[ \text{Area} = \frac{1}{2} \times 60 = 30 \, \text{cm}^2 \]

5. **Conclusion**:
The area of the rhombus is \(30 \, \text{cm}^2\).