jmc

If circle $Q$ has diameter $4$, then so do congruent circles $P$ and $R$. Draw a diameter through $P$ parallel to $AD$. The diameter will be congruent to $AD$, and thus $AD=4$, which is the height of the rectangle. Draw a horizontal line $PQR$ that extends to the sides of the rectangle. This line is $2$ diameters long, so it has length $4\cdot 2=8$. It is parallel and congruent to $AB$, so the width of the rectangle is $8$. Thus, the area of the rectangle is $lw=4\cdot 8=32$, and the answer is $\boxed{32}$.