If `side(a)=4` then area of the equilateral triangle `DeltaABC` is equal to

Options

A. a) `(3sqrt2)/(2)`
B. b) `3`
C. c) `4sqrt3`
D. d) `3sqrt2`

Answer

To find the area of an equilateral triangle with a given side length, we can use the formula for the area of an equilateral triangle:

\[ \text{Area} = \frac{\sqrt{3}}{4} a^2 \]

where \( a \) is the length of a side of the triangle.

### Step-by-step Solution:

1. **Identify the side length**:
Given that \( a = 4 \).

2. **Substitute the value into the formula**:
\[ \text{Area} = \frac{\sqrt{3}}{4} \times (4)^2 \]

3. **Calculate \( (4)^2 \)**:
\[ (4)^2 = 16 \]

4. **Substitute \( 16 \) back into the area formula**:
\[ \text{Area} = \frac{\sqrt{3}}{4} \times 16 \]

5. **Simplify the expression**:
\[ \text{Area} = \frac{16}{4} \sqrt{3} = 4\sqrt{3} \]

6. **Final answer**:
The area of triangle ABC is \( 4\sqrt{3} \) square units.

### Conclusion:
Therefore, the area of the equilateral triangle \( \Delta ABC \) is \( 4\sqrt{3} \).