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 the formula for the area of an equilateral triangle:

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

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

### Step 1: Identify the side length
The side length \( a \) is given as \( 6\sqrt{3} \) cm.

### Step 2: Substitute the side length into the area formula
Substituting \( a = 6\sqrt{3} \) into the area formula:

\[ \text{Area} = \frac{\sqrt{3}}{4} (6\sqrt{3})^2 \]

### Step 3: Calculate \( (6\sqrt{3})^2 \)
Calculating \( (6\sqrt{3})^2 \):

\[ (6\sqrt{3})^2 = 6^2 \cdot (\sqrt{3})^2 = 36 \cdot 3 = 108 \]

### Step 4: Substitute back into the area formula
Now substitute \( 108 \) back into the area formula:

\[ \text{Area} = \frac{\sqrt{3}}{4} \cdot 108 \]

### Step 5: Simplify the expression
Simplifying the expression:

\[ \text{Area} = \frac{108\sqrt{3}}{4} = 27\sqrt{3} \]

### Step 6: Substitute the value of \( \sqrt{3} \)
Now, substitute \( \sqrt{3} = 1.732 \):

\[ \text{Area} = 27 \cdot 1.732 \]

### Step 7: Calculate the final area
Calculating the final area:

\[ \text{Area} = 46.764 \text{ cm}^2 \]

Thus, the area of the equilateral triangle is \( 46.764 \text{ cm}^2 \).

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