This page describes how to derive the forumula for the area of a trapezoid by creating a parallelogram from two congruent trapezoids. The formula is simply one half the area of this parallelogram.
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When the two trapezoids are combined in this way, the result is a parallelogram, which has two pairs of opposite, congruent sides.
Recall that the area of a parallelogram is its altitude (h) times the length of either base. From the figure above we see that both base lengths are equal to b1+b2. So the area of the parallelogram is Since this is the area of two trapezoids we have to divide this by two, giving
This can be rearranged into more familar forms: or