The area of the blue outer ring is given by the area of the entire circular archery less the area of the inner pink circle.
The area of a circle is given by
![Area=\pi r^2](https://img.qammunity.org/2019/formulas/mathematics/high-school/jneqikqpmnwb6ck3geh80dxmw97pomzopc.png)
, where
![r= (d)/(2)](https://img.qammunity.org/2019/formulas/mathematics/high-school/73ig3wwuhlvu5aorwc79ciefdgj4b52gts.png)
, r is the radius, d is the diameter.
Therefore, the area of the outer blue ring is given by:
![Area=\pi\left( (24)/(2) \right)^2-\pi\left( (6)/(2) \right)^2 \\ \\ =\pi(12^2-3^2)=\pi(144-9) \\ \\ =135\pi\ in^2](https://img.qammunity.org/2019/formulas/mathematics/high-school/ku5xvathni8fha0p4r375fkd4qqedkxyr7.png)