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It works because a trapezoid is made up of two triangles , both with the same altitude, that altitude being the height of the trapezoid. If the bases ( i.e parallel sides are a and b and the height is h. one triangle has area 1/2ah and the other 1/2 bh so the total area is

1/2ah+ 1/2bh = 1/2h(a+b).

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Q: Why does the area formula for a trapizoid work?
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