Two adjacent sides of a parallelogram are 12 cm and 9 cm and one of the angle is `30^@` . Find the area of parallelogram.

Options

A. 27 sq. cm
B. 54 sq. cm
C. 108 sq. cm
D. 96 sq. cm

Answer

To find the area of a parallelogram given two adjacent sides and the angle between them, we can use the formula:

\[ \text{Area} = a \times b \times \sin(\theta) \]

where:
- \( a \) and \( b \) are the lengths of the adjacent sides,
- \( \theta \) is the angle between the sides.

### Step-by-Step Solution:

1. **Identify the lengths of the sides and the angle**:
- Let \( a = 12 \) cm (one side),
- Let \( b = 9 \) cm (the adjacent side),
- Let \( \theta = 30^\circ \) (the angle between the sides).

2. **Substitute the values into the area formula**:
\[ \text{Area} = 12 \times 9 \times \sin(30^\circ) \]

3. **Calculate \( \sin(30^\circ) \)**:
- We know that \( \sin(30^\circ) = \frac{1}{2} \).

4. **Substitute \( \sin(30^\circ) \) into the area formula**:
\[ \text{Area} = 12 \times 9 \times \frac{1}{2} \]

5. **Perform the multiplication**:
- First, calculate \( 12 \times 9 = 108 \).
- Then, multiply by \( \frac{1}{2} \):
\[ \text{Area} = 108 \times \frac{1}{2} = 54 \text{ cm}^2 \]

6. **Conclusion**:
- The area of the parallelogram is \( 54 \text{ cm}^2 \).

### Final Answer:
The area of the parallelogram is \( 54 \text{ cm}^2 \).