You may remember from a couple of years ago the math-fun discussion of what one gets when one intersects a cube with a random plane that intersects it nontrivially (Subject: Random slice of a cube). Thanks to communal effort, we learned that the expected number of sides is exactly 4, and that this remains true even if one preselects the orientation of the plane. In preparing to give a public talk about this result (see https://www.cityguideny.com/event/MoMath--National-Museum-of-Mathematics--20...), I realized that some members of the audience may ask "What about the expected area of the intersection? What about the expected perimeter?" The answer to the first question is nice (2/3 times the square of the side-length; ask me if you want to know why). I don't know the answer to the second question, but maybe some of you can help me figure it out (e.g., maybe Keith Lynch can dust off his code and use it to estimate expected perimeter). And while we're at it, numerical corroboration of the answer to the first question would be reassuring. For these two questions, it does NOT suffice to focus on one particular orientation of the cutting plane; you have to average over all of them. The measure I'm using is the unique rotationally-invariant and translationally-invariant continuous measure on the affine Grassmannian (the set of all planes in R^3); it's not a probability measure, but it assigns finite measure to the set of all planes passing through a fixed cube, so by renormalizing you can get a probability measure. By the way, one of the themes of my talk is the collaborative process by which math is done (in contrast to the myth of the isolated genius), so the sequence of events that brought these results to light is going to be integral to my talk. If you have any concerns that I might acknowledge your contribution and for some reason you don't want me to, please let me know! Jim Propp