The area of the strip

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Let $\gamma$ be a convex smooth plane curve of length $l$.
I need to compute the area of the strip swept by the outer normal segments of length $r$ to $\gamma$ and the length of the outer boundary oval of the strip. I assume that a parameterization of the curve is given. But in any case, I have no idea how to decide. I tried to do this for the circle, but it didn't work either.