Area of Annulus

Theorem
Let $A$ be an annulus whose inner radius is $r$ and whose outer radius is $R$.

The area of $A$ is given by:


 * $\map \Area A = \pi \paren {R^2 - r^2}$

Proof

 * Annulus.png

The area of $A$ is seen to be:
 * the area of the outer circle with the area of the inner circle removed.

From Area of Circle:
 * the area of the outer circle is $\pi R^2$
 * the area of the inner circle is $\pi r^2$

The result follows.