The side of an equilateral triangle is ` 6sqrt(3)` cm. Find the area of the triangle. [Take `sqrt(3)=1.732`]

Answer

To find the area of an equilateral triangle with a side length of \( 6\sqrt{3} \) cm, we can use Heron's formula. However, for an equilateral triangle, there is a simpler formula to calculate the area.

### Step-by-Step Solution:

1. **Identify the side length (a)**:
The side length of the equilateral triangle is given as:
\[ a = 6\sqrt{3} \text{ cm} \]

2. **Use the formula for the area of an equilateral triangle**:
The area \( A \) of an equilateral triangle can be calculated using the formula:
\[ A = \frac{\sqrt{3}}{4} a^2 \]

3. **Calculate \( a^2 \)**:
First, we need to calculate \( a^2 \):
\[ a^2 = (6\sqrt{3})^2 = 36 \times 3 = 108 \]

4. **Substitute \( a^2 \) into the area formula**:
Now substitute \( a^2 \) into the area formula:
\[ A = \frac{\sqrt{3}}{4} \times 108 \]

5. **Calculate the area**:
\[ A = \frac{108\sqrt{3}}{4} = 27\sqrt{3} \]

6. **Substitute the value of \( \sqrt{3} \)**:
Given \( \sqrt{3} = 1.732 \), we can find the numerical value of the area:
\[ A = 27 \times 1.732 = 46.764 \text{ cm}^2 \]

### Final Answer:
The area of the equilateral triangle is approximately \( 46.764 \text{ cm}^2 \).