Given a trapezoid, if you double the height and the bases, what happens to the area?

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Answer 1 · 2015-11-14T04:05:04

If you double the height and bases of a trapezoid, the area quadruples.

The area $A$ of a trapezoid with bases $b_1$ and $b_2$ and height $h$ is given by
$A = (b_1+b_2)/2h$

Then, let's consider the area $A'$ of a trapezoid with bases $2b_1$ and $2b_2$ and height $2h$

$A' = (2b_1 + 2b_2)/2(2h) = (2(b_1+b_2))/2(2h) = 4(b_1+b_2)/2h=4A$

Thus the area quadruples.