The diagonals of a rhombus are 7.5 cm and 12 cm. Findits area.

Options

A. 42`cm^2`
B. 45`cm^2`
C. 49`cm^2`
D. 48`cm^2`

Explanation

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 \( d_1 = 7.5 \, \text{cm} \)
- Given \( d_2 = 12 \, \text{cm} \)

2. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \times 7.5 \times 12 \]

3. **Calculate the product of the diagonals**:
\[ 7.5 \times 12 = 90 \]

4. **Multiply by \(\frac{1}{2}\)**:
\[ \text{Area} = \frac{1}{2} \times 90 = 45 \, \text{cm}^2 \]

5. **Final answer**:
The area of the rhombus is \( 45 \, \text{cm}^2 \).