In `DeltaABCifa=2x,b=2yandangleC=120^(@)`, then the area of the triangle is

Options

A. xy sq units
B. xy `sqrt(3)` sq units
C. 3xy sq units
D. 2xy sq units

Explanation

To find the area of triangle ABC given the angles and sides, we can use the formula for the area of a triangle when two sides and the included angle are known. The formula is:

\[ \text{Area} = \frac{1}{2}ab \sin(C) \]

Where:
- \( a \) and \( b \) are the lengths of the two sides,
- \( C \) is the included angle between those two sides.

### Given:
- \( a = 2x \)
- \( b = 2y \)
- \( C = 120^\circ \)

### Step-by-step Solution:

1. **Identify the sides and angle**:
- We have \( a = 2x \), \( b = 2y \), and \( C = 120^\circ \).

2. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \cdot (2x) \cdot (2y) \cdot \sin(120^\circ) \]

3. **Calculate \( \sin(120^\circ) \)**:
- We know that \( \sin(120^\circ) = \sin(180^\circ - 60^\circ) = \sin(60^\circ) = \frac{\sqrt{3}}{2} \).

4. **Substitute \( \sin(120^\circ) \) back into the area formula**:
\[ \text{Area} = \frac{1}{2} \cdot (2x) \cdot (2y) \cdot \frac{\sqrt{3}}{2} \]

5. **Simplify the expression**:
\[ \text{Area} = \frac{1}{2} \cdot 4xy \cdot \frac{\sqrt{3}}{2} = \frac{4xy\sqrt{3}}{4} = xy\sqrt{3} \]

### Final Result:
The area of triangle ABC is:
\[ \text{Area} = xy\sqrt{3} \]