If the height of the equilateral triangle is `2sqrt(3) cm`, then determine the area (in `cm^2`) of the equilateral triangle.

Options

A. `6`
B. `2sqrt(3)`
C. `4sqrt(3)`
D. `12`

Answer

To find the area of an equilateral triangle given its height, we can use the formula for the area of an equilateral triangle in terms of its height \( h \):

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

### Step-by-Step Solution:

1. **Identify the height of the triangle**: The height \( h \) of the equilateral triangle is given as \( 2\sqrt{3} \) cm.

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

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**:
\[ \text{Area} = \frac{12}{\sqrt{3}} \]

5. **Rationalize the denominator**:
\[ \text{Area} = \frac{12 \cdot \sqrt{3}}{3} = 4\sqrt{3} \]

6. **Final answer**: The area of the equilateral triangle is \( 4\sqrt{3} \) cm².