The diagonals of a rhombus are respectively 6 cm and 12 cm . Its area (in `cm^2`) is equal to :

Options

A. 24
B. 36
C. 8
D. 12

Answer

To find the area of a rhombus given its diagonals, 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**:
- Let \(d_1 = 6 \, \text{cm}\) (the first diagonal).
- Let \(d_2 = 12 \, \text{cm}\) (the second diagonal).

2. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \times d_1 \times d_2 = \frac{1}{2} \times 6 \times 12 \]

3. **Calculate the product of the diagonals**:
\[ 6 \times 12 = 72 \]

4. **Multiply by \(\frac{1}{2}\)**:
\[ \text{Area} = \frac{1}{2} \times 72 = 36 \, \text{cm}^2 \]

Thus, the area of the rhombus is \(36 \, \text{cm}^2\).