The diagonals of a rhombus are 7.5 cm and 12 cm. Find its 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 follow these steps:

### Step-by-Step Solution:

1. **Identify the lengths of the diagonals**:
- Let \( D_1 = 7.5 \, \text{cm} \) (the first diagonal)
- Let \( D_2 = 12 \, \text{cm} \) (the second diagonal)

2. **Write down the formula for the area of a rhombus**:
- The formula for the area \( A \) of a rhombus in terms of its diagonals is:
\[ A = \frac{1}{2} \times D_1 \times D_2 \]

3. **Substitute the values of the diagonals into the formula**:
- Substitute \( D_1 \) and \( D_2 \) into the formula:
\[ A = \frac{1}{2} \times 7.5 \times 12 \]

4. **Calculate the product of the diagonals**:
- First, calculate \( 7.5 \times 12 \):
\[ 7.5 \times 12 = 90 \]

5. **Multiply by \( \frac{1}{2} \)**:
- Now, calculate the area:
\[ A = \frac{1}{2} \times 90 = 45 \, \text{cm}^2 \]

6. **Conclusion**:
- Therefore, the area of the rhombus is \( 45 \, \text{cm}^2 \).