Let the radius of the circle be $r$. The half circumference is $\pi r$ and the diameter is $2r$. Given that $\pi r - 2r = 4$. Factoring out $r$, we get $r(\pi - 2) = 4$. Substituting $\pi = \frac{22}{7}$, we have $r(\frac{22}{7} - 2) = 4 \implies r(\frac{22 - 14}{7}) = 4 \implies r(\frac{8}{7}) = 4$. Solving for $r$, $r = 4 \times \frac{7}{8} = \frac{7}{2}$ cm. The area of the circle is $A = \pi r^2 = \frac{22}{7} \times (\frac{7}{2})^2 = \frac{22}{7} \times \frac{49}{4} = \frac{22 \times 7}{4} = \frac{11 \times 7}{2} = \frac{77}{2} = 38.5$ sq.cm.