Let's start by recalling the formula for the area of a circle with a radius r.
A=π r^2
It is given that the bicycle tire has a diameter of 26 inches. Dividing this value by 2, we can find the radius of the tire.
r=26/2=13in
Now, we can substitute r with 13 into the formula and calculate the area of the tire.
Finally, since the decoration covers 19 of the tire, if we divide the area of the circle by 9 we will determine the area of the decoration.
\begin{aligned}
A_\text{decoration}=\dfrac{531}{9}=59\text{ in}^2
\end{aligned}
