3. In the given figure, $A B C D$ is a square with sides of length 4 , and $Q$ is the midpoint of $C D$. $A B C D$ is reflected along the line $A Q$ to give the square $A B^{\prime} C^{\prime} D^{\prime}$. The two squares overlap in the quadrilateral $A D Q D^{\prime}$. Determine the area of quadrilateral $A D Q D^{\prime}$.
Solution: Since the side length of $A B C D$ is 4 , so $D Q=2$. The area of $A D Q$ is $4 \times 2 / 2=4$ and by symmety the area of $A D^{\prime} Q$ is the same. Thus, the area of $A D Q D^{\prime}$ is $4+4=8$.