How do you figure out the area of a trapezium

Hello,
Let assume B' the image of B by the translation DC.

The trapezium ABCD is composed of area I,area II, area III.
Area III is equal to area IV.
the area of a trapezium is equal to area I+ area II+ area IV which is a triangle with base =AB and h the height.
the area of a trapezium= (AB+BB')*h/2=(AB+DC)*h/2