3. In parallelogram $A B C D$, $P$ is the midpoint of $B C$, a line through $P$ parallel to $B D$ intersects $C D$ at $Q$, and $P A, P D, Q A, Q B$ are connected. Among the triangles in the figure, apart from $\triangle A B P$, how many triangles have the same area as $\triangle A B P$?
(A) three;
(B) four;
(C) five;
(D) six.
3. (C)

Given the conditions, $Q$ is the midpoint of $CD$, so there are three types of triangles in the figure that have the same area as $\triangle ABP$:
(1) Two triangles that are equal in base and height to $\triangle ABP$: $\triangle BPD$, $\triangle PCD$.
(2) Two triangles with one side twice the length of $BP$ and the height half of the height on $BP$: $\triangle BCQ$, $\triangle ADQ$.
(3) One triangle that is equal in base and height to $\triangle BCQ$: $\triangle QDB$. Therefore, there are five in total.