Question

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

Answer 1

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

Explanation:

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.