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Here's a trapezium I've drawn. I drew a line through it at half the height, then drew perpendiculars bisecting the non-parallel sides. The parallel side lengths are a and b:
Now let's move things around a bit:
The bottom is now (a+b) and the height of the coloured area is half the height of the original trapezium, so the area is half the product of the trapezium's height and the sum of the lengths of its parallel sides.
Stephen La Rocque.>