ABCD is a parallelogram and m `angleDAB=30^@`, BC=20 cm and AB=20 cm. Find the area of parallelogram:

Options

A. `150 cm^2`
B. `200 cm^2`
C. `400 cm^2`
D. `260 cm^2`

Answer

To find the area of the parallelogram ABCD, we can use the formula for the area of a parallelogram, which is given by:

\[ \text{Area} = \text{base} \times \text{height} \]

However, since we have the angle and the lengths of the sides, we can also use the formula:

\[ \text{Area} = AB \times AD \times \sin(\angle DAB) \]

### Step 1: Identify the given values
- \( AB = 20 \, \text{cm} \)
- \( AD = 20 \, \text{cm} \) (since opposite sides of a parallelogram are equal)
- \( \angle DAB = 30^\circ \)

### Step 2: Calculate the sine of the angle
We need to find \( \sin(30^\circ) \):
\[ \sin(30^\circ) = \frac{1}{2} \]

### Step 3: Substitute the values into the area formula
Now, we can substitute the values into the area formula:
\[ \text{Area} = AB \times AD \times \sin(\angle DAB) = 20 \, \text{cm} \times 20 \, \text{cm} \times \frac{1}{2} \]

### Step 4: Perform the multiplication
Calculating the area:
\[ \text{Area} = 20 \times 20 \times \frac{1}{2} = 400 \times \frac{1}{2} = 200 \, \text{cm}^2 \]

### Final Answer
The area of the parallelogram ABCD is \( 200 \, \text{cm}^2 \).

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