To find the area of triangle $\Delta ABC$ given the sides $b = 28$ cm, $c = 14$ cm, and the angle $A = 30^\circ$, we can use the formula for the area of a triangle when two sides and the included angle are known:

$\text{Area} = \frac{1}{2} \times b \times c \times \sin(A)$

Substituting the given values:

$\text{Area} = \frac{1}{2} \times 28 \times 14 \times \sin(30^\circ)$

We know that $\sin(30^\circ) = \frac{1}{2}$:

$\text{Area} = \frac{1}{2} \times 28 \times 14 \times \frac{1}{2}$

$\text{Area} = \frac{1}{2} \times 28 \times 14 \times \frac{1}{2} = 98 \text{ cm}^2$

Thus, the area of $\Delta ABC$ is $98$ square centimeters.

The correct answer is:

$\boxed{98 \text{ centimeters}^2}$

Would you like more details or have any questions?

Here are some related questions:

1. How do you derive the sine rule for calculating the area of a triangle?
2. What would be the area if angle A were 60 degrees instead of 30 degrees?
3. How does the area change if both sides $b$ and $c$ are doubled?
4. How can you find the area of a triangle if only one side and two angles are given?
5. What is the relationship between the area of a triangle and its perimeter?

Tip: When given two sides and the included angle in a triangle, the sine rule is a quick and effective way to find the area.