The adjacent sides of parallelogram are 6 cm and 4 cm and the angle between them is `30^@`.The area of the parallelogram is -----

Options

A. `12 cm^2`
B. `24 cm^2`
C. `48 cm^2`
D. None of these

Answer

To find the area of the parallelogram, 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.

Given:
- \( a = 6 \) cm,
- \( b = 4 \) cm,
- \( \theta = 30^\circ \).

Now, let's calculate the area step by step:

### Step 1: Identify the values
We have:
- \( a = 6 \) cm,
- \( b = 4 \) cm,
- \( \theta = 30^\circ \).

### Step 2: Calculate \( \sin(30^\circ) \)
Using the known value:
\[ \sin(30^\circ) = \frac{1}{2} \]

### Step 3: Substitute the values into the area formula
Now we can substitute the values into the area formula:
\[ \text{Area} = 6 \times 4 \times \sin(30^\circ) \]
\[ \text{Area} = 6 \times 4 \times \frac{1}{2} \]

### Step 4: Perform the multiplication
Calculating the multiplication:
\[ \text{Area} = 6 \times 4 = 24 \]
\[ \text{Area} = 24 \times \frac{1}{2} = 12 \text{ cm}^2 \]

### Final Answer
The area of the parallelogram is \( 12 \text{ cm}^2 \).

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