“An equilateral triangle has side length 6. What is the area of the region containing all points that are outside the triangle but not more than 3 units from a point of the triangle?”

Of course we had to dig out our old 3d printed objects to start the problem, and then my son drew in the analogous 2 dimensional figures:

Next we moved to a second sheet of paper and my son solved the problem. I like his “inclusion / exclusion” way of counting the area here, though I understand that some people would probably prefer a more geometric approach.

How fun to have one of our old 3d printing projects help us solve a challenging AMC 10 problem!