Explanation:

- To find the area of an equilateral triangle with side length \( s \), use the formula:

$$ \text{Area} = \frac{\sqrt{3}}{4} s^2 $$

- Given: Side \( s = 14 \, \text{cm} \).

- Calculate the area:

$$ \text{Area} = \frac{\sqrt{3}}{4} \times 14^2 $$

$$ = \frac{\sqrt{3}}{4} \times 196 $$

$$ = 49\sqrt{3} \, \text{cm}^2 $$

- Option 1: \( 64\sqrt{3} \) - Incorrect

- Option 2: \( 49\sqrt{2} \) - Incorrect

- Option 3: \( 64\sqrt{2} \) - Incorrect

- Option 4: \( 49\sqrt{3} \) - Correct

- The correct answer is \(\mathbf{49\sqrt{3}}\).

Option 4 is correct.