The area of an equilateral triangle with side `2sqrt3` cm is

Options

A. `5.196" "cm^(2)`
B. `0.866" "cm^(2)`
C. `3.496" "cm^(2)`
D. `1.732" "cm^(2)`

Explanation

To find the area of an equilateral triangle with a side length of \(2\sqrt{3}\) cm, 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**:
The side length \(a\) of the equilateral triangle is given as \(2\sqrt{3}\) cm.

2. **Substitute the side length into the area formula**:
We substitute \(a = 2\sqrt{3}\) into the area formula:
\[ \text{Area} = \frac{\sqrt{3}}{4} (2\sqrt{3})^2 \]

3. **Calculate \((2\sqrt{3})^2\)**:
\[ (2\sqrt{3})^2 = 2^2 \cdot (\sqrt{3})^2 = 4 \cdot 3 = 12 \]

4. **Substitute back into the area formula**:
Now substitute \(12\) back into the area formula:
\[ \text{Area} = \frac{\sqrt{3}}{4} \cdot 12 \]

5. **Simplify the expression**:
\[ \text{Area} = \frac{12\sqrt{3}}{4} = 3\sqrt{3} \]

6. **Calculate the numerical value of \(3\sqrt{3}\)**:
Using the approximation \(\sqrt{3} \approx 1.732\):
\[ 3\sqrt{3} \approx 3 \cdot 1.732 = 5.196 \]

7. **Final result**:
Therefore, the area of the equilateral triangle is approximately \(5.196\) cm².

### Summary:
The area of the equilateral triangle with side \(2\sqrt{3}\) cm is \(5.196\) cm².