Find the area of an equilateral triangle whose side is ` 4sqrt(3) ` cm.

Answer

To find the area of an equilateral triangle with a side length of \( 4\sqrt{3} \) cm, we can follow these steps:

### Step 1: Identify the formula for the area of an equilateral triangle.
The formula for the area \( A \) of an equilateral triangle with side length \( a \) is given by:
\[ A = \frac{\sqrt{3}}{4} a^2 \]

### Step 2: Substitute the side length into the formula.
In this case, the side length \( a \) is \( 4\sqrt{3} \) cm. We will substitute this value into the formula:
\[ A = \frac{\sqrt{3}}{4} (4\sqrt{3})^2 \]

### Step 3: Calculate \( (4\sqrt{3})^2 \).
Now, we need to calculate \( (4\sqrt{3})^2 \):
\[ (4\sqrt{3})^2 = 4^2 \cdot (\sqrt{3})^2 = 16 \cdot 3 = 48 \]

### Step 4: Substitute back into the area formula.
Now we substitute \( 48 \) back into the area formula:
\[ A = \frac{\sqrt{3}}{4} \cdot 48 \]

### Step 5: Simplify the expression.
To simplify, we can divide \( 48 \) by \( 4 \):
\[ A = \sqrt{3} \cdot 12 = 12\sqrt{3} \]

### Final Answer:
Thus, the area of the equilateral triangle is:
\[ \boxed{12\sqrt{3}} \text{ cm}^2 \]

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