42. As shown in the figure, in isosceles trapezoid $A B C D$, $A D / / B C, \angle B=45^{\circ}, P$ is a point on side $B C$, the area of $\triangle P A D$ is $\frac{1}{2}, \angle A P D=90^{\circ}$, then the minimum value of $A D$ is $\qquad$
Answer: $\sqrt{2}$