Assertion : If the diagonals of a rhombus are 8 cm and 12 cm, then the area of rhombus is given by 96 `cm^(2)`.
Reason : Area o f rhombus is 1/2 `xx d_(1) xx d_(2)` where `d_(1)` and `d_(2)` are the lengths of the diagonals.

Options

A. If both assertion and reason are tme and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is trne.

Answer

To solve the problem, we need to determine whether the assertion and reason provided are true or false.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that if the diagonals of a rhombus are 8 cm and 12 cm, then the area of the rhombus is 96 cm².

2. **Understanding the Reason**:
The reason provided states that the area of a rhombus can be calculated using 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.

3. **Calculating the Area of the Rhombus**:
Given:
- \(d_1 = 8 \, \text{cm}\)
- \(d_2 = 12 \, \text{cm}\)

Using the formula for the area:
\[ \text{Area} = \frac{1}{2} \times 8 \times 12 \]
\[ = \frac{1}{2} \times 96 \]
\[ = 48 \, \text{cm}^2 \]

4. **Evaluating the Assertion**:
The calculated area of the rhombus is 48 cm², not 96 cm². Therefore, the assertion is **false**.

5. **Evaluating the Reason**:
The reason provided is correct as it accurately describes how to calculate the area of a rhombus using its diagonals.

### Conclusion:
- The assertion is **false**.
- The reason is **true**.