4. (10 points) The width of rectangle $O_{1} O_{2} B A$ is $A O_{1}=1$ cm. Circles $O_{1}$ and $O_{2}$ are drawn with centers at $O_{1}$ and $O_{2}$, respectively, and a radius of 1 cm, intersecting line segment $O_{1} O_{2}$ at points $C$ and $D$, as shown in the figure. What is the area of quadrilateral $A B C D$ in square centimeters?
【Analysis】According to the problem, we can draw $D E \perp A B$ at $E$. It is easy to know that $A E=O_{1} D=O_{2} C$, and the areas of $\triangle A E D$ and $\triangle B C O_{2}$ are equal. Therefore, the area of the shaded part in the figure is equal to the area of the square $E B O_{2} D$. It is not difficult to find the area of the shaded part.

【Solution】According to the analysis, as shown in the figure, draw $D E \perp A B$ at $E$. It is easy to know that $A E=O_{1} D=O_{2} C$, and the areas of $\triangle A E D$ and $\triangle B C O_{2}$ are equal,

Therefore, the area of the shaded part in the figure is equal to the area of the square $E B O_{2} D$ $=1 \times 1=1$ (square centimeter). Hence, the answer is: 1