Puzzle: diagonals in a polygon – simpler versions
March 28, 2007 am31 7:33 am
How many diagonals are in a polygon?
This space is for the most challenging task: designing easier versions (or variations) of this problem. Post them here.
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JD2718 
One simplification for middle school students would be to ask for the number of diagonals in a specific polygon. Make it one that would be too confusing to sketch, but not too hard to count up the diagonals systematically once they notice the pattern—maybe 15 or 20 sides.
For younger students, just drawing all the diagonals in a pentagon or hexagon can be a challenge—and then it is fun to color in the resulting design.
I never thought of that as a challenge: just drawing them all.
Kids do have trouble drawing the polygons. I tell them to draw a circle, and to distribute n vertices around it (not necessarily evenly) to get a relatively nice, convex polygon.
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