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If you mean the area, this can be derived in different ways. Most school books should show some derivation of the formula.* It's quite easy to see intuitively (though perhaps a bit more tricky to prove) that the area should be equivalent to the corresponding rectangle, where the width of the rectangle is set equal to the average width of the trapezium. The average, in this case, is the average of the longer and the shorter side (of the two parallel sides). Perhaps the formula was originally derived this way, though it's hard to be sure.

* You can divide a trapezium into rectangles and triangles, and derive the formula from there.

* Of course you could also use integration, though in this case, this is more complicated than necessary.

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The answer depends on what the formula is supposed to refer to: the perimeter, the area, the angle sum?

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9y ago
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Q: How was the formula of the trapezium made?
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