Trapezoid/Trapezium Area Formula, A= (a+b) × h /2, why?

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Trapezoid/Trapezium Area, A= (a+b) × h /2, why? Given any trapezoid, if the parallel top and bottom are a and b, respectively, and the corresponding height (altitude) is h, the area is (a+b) × h /2. But why? To see why, we take two congruent copies of a trapezoid and make a parallelogram with the same height and a base of (a+b). Such a parallelogram can be easily converted to a rectangle with a base of (a+b) and height (h, or width), and, accordingly, an area of (a+b) × h. Why do we have to divide that by 2? Well, it is because we want to know the area of the trapezoid. Of course, there are other ways to explain it. One way or the other, it goes back to what we know about rectangles or other shapes. Two versions are provided to demonstrate the process behind A= (a+b) × h /2. The trapezoid is just a random one. Have fun.