A square of side length $4 \mathrm{~cm}$ is given. The boundary of the shaded region is defined by one semi-circle on the top and two circular arcs at the bottom, each of radius $2 \mathrm{~cm}$, as shown.
The area of the shaded region is__________$\text{cm}^{2}.$
- $8$
- $4$
- $12$
- $10$