Find the area of a regular hexagon of side 6 cm .

Answer

To find the area of a regular hexagon with a side length of 6 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-by-Step Solution:

1. **Identify the side length:**
- The side length \( s \) of the hexagon is given as 6 cm.

2. **Substitute the side length into the formula:**
- Plug \( s = 6 \) cm into the area formula:
\[ \text{Area} = \frac{3\sqrt{3}}{2} (6)^2 \]

3. **Calculate \( (6)^2 \):**
- Calculate the square of the side length:
\[ (6)^2 = 36 \]

4. **Multiply by \( \frac{3\sqrt{3}}{2} \):**
- Now substitute \( 36 \) back into the formula:
\[ \text{Area} = \frac{3\sqrt{3}}{2} \times 36 \]

5. **Simplify the multiplication:**
- Calculate \( \frac{3 \times 36}{2} \):
\[ \frac{3 \times 36}{2} = \frac{108}{2} = 54 \]
- Thus, we have:
\[ \text{Area} = 54\sqrt{3} \text{ cm}^2 \]

6. **Final result:**
- The area of the regular hexagon is:
\[ \text{Area} = 54\sqrt{3} \text{ cm}^2 \]