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

Options

A. `147sqrt(3)`
B. `441sqrt(3)`
C. `196sqrt(3)`
D. `294sqrt(3)`

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:

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

### Step 1: Identify the side length
The side length of the hexagon is given as 14 cm.

### Step 2: Substitute the side length into the area formula
Now, we substitute the side length into the formula:

\[ \text{Area} = \frac{3\sqrt{3}}{2} \times (14)^2 \]

### Step 3: Calculate \(14^2\)
First, we calculate \(14^2\):

\[ 14^2 = 196 \]

### Step 4: Substitute back into the area formula
Now we substitute \(196\) back into the formula:

\[ \text{Area} = \frac{3\sqrt{3}}{2} \times 196 \]

### Step 5: Simplify the expression
Next, we simplify the expression:

\[ \text{Area} = \frac{3 \times 196 \sqrt{3}}{2} \]

### Step 6: Calculate \(3 \times 196\)
Now we calculate \(3 \times 196\):

\[ 3 \times 196 = 588 \]

### Step 7: Divide by 2
Now we divide \(588\) by \(2\):

\[ \frac{588}{2} = 294 \]

### Step 8: Final area expression
Thus, the area of the hexagon is:

\[ \text{Area} = 294\sqrt{3} \text{ cm}^2 \]

### Final Answer
The area of the regular hexagon is \(294\sqrt{3} \text{ cm}^2\).

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