The radius of the semicircle $=14$, and the area of the shaded region $\(=2 \times \frac{1}{2} \times \pi \times r^2=2 \times \frac{\pi}{2} \times 7^2\)$ The percentage of the area of the shaded region to the area of the semi-circle $\(=\frac{2 \times \frac{1}{2} \times \pi \times 7^2}{\frac{1}{2} \times \pi \times 14^2}=\frac{1}{2}=50 \%\)$.

Therefore, the correct answer is $D$.