The area of a regular hexagon of side `2sqrt(3)` cm is :

Options

A. `18sqrt(3) cm^(2)`
B. `12sqrt(3) cm^(2)`
C. `36sqrt(3) cm^(2)`
D. `27sqrt(3) cm^(2)`

Answer

To find the area of a regular hexagon with a side length of \( 2\sqrt{3} \) cm, we can use the formula for the area of a regular hexagon:

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

where \( s \) is the length of a side of the hexagon.

### Step 1: Identify the side length
The side length \( s \) of the hexagon is given as \( 2\sqrt{3} \) cm.

### Step 2: Substitute the side length into the area formula
Now, we substitute \( s = 2\sqrt{3} \) into the area formula:

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

### Step 3: Calculate \( (2\sqrt{3})^2 \)
We calculate \( (2\sqrt{3})^2 \):

\[ (2\sqrt{3})^2 = 2^2 \cdot (\sqrt{3})^2 = 4 \cdot 3 = 12 \]

### Step 4: Substitute back into the area formula
Now we substitute this value back into the area formula:

\[ \text{Area} = \frac{3\sqrt{3}}{2} \cdot 12 \]

### Step 5: Simplify the expression
Now we simplify the expression:

\[ \text{Area} = \frac{3\sqrt{3} \cdot 12}{2} = \frac{36\sqrt{3}}{2} = 18\sqrt{3} \]

### Final Answer
Thus, the area of the regular hexagon is:

\[ \text{Area} = 18\sqrt{3} \text{ cm}^2 \]

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