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 $A D Q D^{\prime}$.