Geometry Fundamentals

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.

Cutting Shapes

                     

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 12\frac12 units wide by 12\frac12 units tall can be formed by cutting the unit square in half width-wise, and then in half again height-wise: