In the last quiz, we saw how we can calculate the area of an unknown shape by sliding it to coincide with a known one:
or by recognizing a known shape in the negative space around an unknown one:
But when these aren't enough, we need to actively manipulate the shape we're interested in to get it into a form we can reason about. In this quiz, we're going to learn an approach for doing this: the cut.
The power of the cut is that it lets us build new shapes out of known ones.
If we can find a way to form our shape of interest by making symmetric cuts to a known shape, then we can relate their areas by how many cuts were required.
For example, a square that's units wide by units tall can be formed by cutting the unit square in half width-wise, and then in half again height-wise: