What is the area (in sq cm) of a regular hexagon of side 14 cm?

Options

A. `147 sqrt3`
B. `441 sqrt3`
C. `196 sqrt3`
D. `294 sqrt3`

Answer

To find the area of a regular hexagon with a side length of 14 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 14 cm.

2. **Substitute the side length into the formula**:
We substitute \( s = 14 \) cm into the area formula:
\[ \text{Area} = \frac{3\sqrt{3}}{2} (14)^2 \]

3. **Calculate \( (14)^2 \)**:
\[ (14)^2 = 196 \]

4. **Multiply by \( \frac{3\sqrt{3}}{2} \)**:
Now we substitute \( 196 \) back into the area formula:
\[ \text{Area} = \frac{3\sqrt{3}}{2} \times 196 \]

5. **Simplify the multiplication**:
First, we can simplify \( \frac{196}{2} \):
\[ \frac{196}{2} = 98 \]
Now, multiply by 3:
\[ 3 \times 98 = 294 \]

6. **Final expression for the area**:
Therefore, the area of the hexagon is:
\[ \text{Area} = 294\sqrt{3} \text{ cm}^2 \]

### Final Answer:
The area of the regular hexagon is \( 294\sqrt{3} \) cm².