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

#####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+