$\mathrm{Az} A B$ as a diameter, a semicircle is drawn over it, and from point $D$ on the circumference of the semicircle, a perpendicular is dropped to $A B$, with the foot of the perpendicular being $C$. Semicircles are then drawn over $A C$ and $C B$ as diameters, resulting in the semicircles $A E C$ and $C F B$. What is the area of the figure $A D B F C E A$, if $D C=a$?
$$
t=\frac{a^{2}}{4} \pi
$$

(L. K. M. L. VII. 42. 1.)

Number of solutions: 55.