Hexagon Area Calculation

Given Information

• Shape: Regular Hexagon
• Side Length ($a$): $2\sqrt{3}$ cm

Area Formula

The area of a regular hexagon with side length '$a$' is calculated using the formula:

Area = $\frac{3\sqrt{3}}{2} a^2$

Calculation Steps

1. Calculate the square of the side length ($a^2$):

   Given $a = 2\sqrt{3}$ cm.

   $a^2 = (2\sqrt{3})^2 = 2^2 \times (\sqrt{3})^2 = 4 \times 3 = 12$ cm$^2$.

2. Substitute $a^2$ into the area formula:

   Area = $\frac{3\sqrt{3}}{2} \times 12$ cm$^2$.

3. Simplify to find the area:

   Area = $3\sqrt{3} \times \frac{12}{2}$ cm$^2$.

   Area = $3\sqrt{3} \times 6$ cm$^2$.

   Area = $18\sqrt{3}$ cm$^2$.

Conclusion

The calculated area of the regular hexagon is $18\sqrt{3}$ cm$^2$. This matches Option 3.