Consider a convex polygon \mathcal{P} in space with perimeter 20 and area 30. What is the volume of the locus of points that are at most 1 unit away from some point in the interior of \mathcal{P}?
Consider a convex polygon \mathcal{P} in space with perimeter 20 and area 30. What is the volume of the locus of points that are at most 1 unit away from some point in the interior of \mathcal{P}?