Area of Annulus as Area of Rectangle

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

The area of $A$ is given by:


 * $\map \Area A = 2 \pi \paren {r + \dfrac w 2} \times w$

where $w$ denotes the width of $A$.

That is, it is the area of the rectangle contained by:
 * the width of $A$
 * the circle midway in radius between the inner radius and outer radius of $A$.

Proof

 * Annulus-mid-circle.png

The result follows from Area of Rectangle.