There is a question that goes as follows:
The locus of $P$ is the interior of an n-sided convex polygon of perimeter $p$, area $\Delta$. The locus of $Q$ is all points where $PQ\leq r$. Find area of locus of $Q$.
($p$, $r$, $n$ and $\Delta$ are known values)
By drawing rectangles and circular arcs around the shape, it is easy enough to prove that the answer is $rp + \pi r^2 + \Delta$.
I think we can say the same result is true for any convex simple closed curve, such as an ellipse. Firstly I'd like to confirm that's true.
Also I'd like to know if there is any simple way of determining the area of locus of $Q$ for a concave polygon (and if so, then what about concave curves?).
And is there any existing material online on this topic? (Ideally not too high-level, but anything's better than nothing)