Geometry Level 2

$$ABCD$$ is a quadrilateral with $$AD=BC,$$ $$AB=40,$$ $$CD=20,$$ and $${\color{blue}m\angle A} + {\color{orange}m\angle B} = 90^\circ.$$

What is the area of quadrilateral $$ABCD?$$

Hint: Consider how copies of $$ABCD$$ can be constructed into another shape.

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