Fitting an Object to a Curve

[ohioandy]

So...I have not yet mastered the shape tool - where I can effectively adjust curves and points (I'm working on it!). With that said, I am seeking to transform my current object (shape of a rectangle) into an area where it bends along a curve (see attached picture). Is there a simpler way to do this (Note, I want to keep the object properties. I.e., I don't want to convert my shape into a bitmap and then do a bitmap fill)?

Thanks for any tips or suggestions!