The lengths of the diagonals of a rhombus are 18 cm and 15 cm. The area of the rhombus is

Options

A. `270 cm^(2)`
B. `135 cm^(2)`
C. `90 cm^(2)`
D. `180 cm^(2)`

Answer

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

\[ \text{Area of rhombus} = \frac{1}{2} \times d_1 \times d_2 \]

where \(d_1\) and \(d_2\) are the lengths of the diagonals.

### Step-by-Step Solution:

1. **Identify the lengths of the diagonals**:
- Given \(d_1 = 18 \, \text{cm}\) and \(d_2 = 15 \, \text{cm}\).

2. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \times d_1 \times d_2 = \frac{1}{2} \times 18 \times 15 \]

3. **Calculate the product of the diagonals**:
- First, calculate \(18 \times 15\):
\[ 18 \times 15 = 270 \]

4. **Multiply by \(\frac{1}{2}\)**:
\[ \text{Area} = \frac{1}{2} \times 270 = 135 \, \text{cm}^2 \]

5. **Final Answer**:
- The area of the rhombus is \(135 \, \text{cm}^2\).