3. Given an isosceles trapezoid $A B C D$ with legs $A B=C D=a, A C \perp B D, \angle A B C=\alpha$. Then the area of this trapezoid is ( )
(A) $2 a \sin \alpha$
(B) $a^{2} \sin ^{2} a$
(C) $2 a \cos \alpha$
(D) $a^{2} \cos \alpha$
3. (B).

As shown in Figure 3, draw $A E \perp B C$, with $E$ as the foot of the perpendicular. Note that $\triangle B O C$ is an isosceles right triangle, so $\triangle A E C$ is also an isosceles right triangle, hence
$$
E C=A E=a \sin \alpha .
$$
$S_{\text {square } A \text { ABDC }}=a^{2} \sin ^{2} \alpha$.