The quadrilateral DB'CD' is a trapezoid with an area of (DD'+B'C)* height /2.

Because the height is fixed, it is only necessary to verify that the value of DD'+B'C is fixed.

No matter how you move, B' is in line BC.

DD'B'B is a parallelogram row.

DD'=BB '

BB'+B'C=BC is a fixed value.

So DD'+B'C is a fixed value.

The area of quadrangle DB'CD' is also a fixed value.

(summarize how to write by yourself, that's the way of thinking. )