HMMT November 2024 T9

Let $P$ be a point inside isosceles trapezoid $A B C D$ with $A B \| C D$ such that

$$\angle P A D=\angle P D A=90^{\circ}-\angle B P C$$

If $P A=14, A B=18$, and $C D=28$, compute the area of $A B C D$.