2. In quadrilateral $A B C D$, it is known that $A B=B C, \angle A B C=$ $\angle A D C=90^{\circ}$. A perpendicular $B H$ is dropped from vertex $B$ to side $A D$. Find the area of quadrilateral $A B C D$, if it is known that $B H=h$.
Answer: $h^{2}$.

![](https://cdn.mathpix.com/cropped/2024_05_06_dfacd005d08f3d07ee49g-2.jpg?height=436&width=526&top_left_y=579&top_left_x=843)

Solution:

Cut off the triangle $A B H$, attach it to the top - we get a square with side $h$.