Last summer James Tanton posted this problem on Twitter:
That problem led to a super fun 3D printing project with the boys:
James Tanton’s Geometry Problem and 3D Printing
To my great (and wonderful) surprise, today my older son and I came across a similar problem from an old AMC 10:
Problem #17 from the 2008 AMC 10A hosted at Art of Problem Solving
Here’s the problem:
“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!