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

Answer

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:**
- First, calculate \(7.5 \times 12\):
\[ 7.5 \times 12 = 90 \]

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 \(45 \, \text{cm}^2\).