Area of annulus from single number

An annulus is a geometric object made up of two circles like this:

The area of the annulus is clearly $$\pi R^2 - \pi r^2=\pi(R^2-r^2)$$ . At first glance we might think it is enough to know the difference $$R-r$$ to calculate the area of the annulus. But, since $$f(x)=x^2$$ is not a linear function this will not work. However, if we store the length of tangent of the inner circle contained in the outer circle, $$t$$ , instead, the area can indeed be deduced from it:

Using pythagoras we can observe that

$R^2=(t/2)^2+r^2\rightarrow t^2/4=R^2-r^2$

and so we can calculate the area as $\pi t^2/4$ .