Area of a regular hexagon with side ‘a’ is

Options

A. `(3 sqrt3)/4 a^2` sq. unit
B. `12/(2sqrt3)a^2` sq. unit
C. `9/(2sqrt3)a^2` sq. unit
D. `6/(sqrt2)a^2` sq. unit

Answer

To find the area of a regular hexagon with side length 'a', we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for the Area of a Regular Hexagon**:
The area \( A \) of a regular hexagon can be calculated using the formula:
\[ A = \frac{3\sqrt{3}}{2} a^2 \]

2. **Substitute the Value of 'a'**:
Since we are given that the side length of the hexagon is 'a', we can directly substitute 'a' into the formula:
\[ A = \frac{3\sqrt{3}}{2} a^2 \]

3. **Rationalize the Expression**:
If required, we can rationalize the expression. To do this, we can multiply both the numerator and the denominator by \(\sqrt{3}\):
\[ A = \frac{3\sqrt{3}}{2} a^2 \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{3 \cdot 3}{2\sqrt{3}} a^2 = \frac{9}{2\sqrt{3}} a^2 \]

4. **Final Expression**:
Thus, the area of the regular hexagon can also be expressed as:
\[ A = \frac{9}{2\sqrt{3}} a^2 \]

### Final Answer:
The area of a regular hexagon with side length 'a' is:
\[ A = \frac{3\sqrt{3}}{2} a^2 \quad \text{or} \quad A = \frac{9}{2\sqrt{3}} a^2 \]

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