Clever Cuts

  • Clever Cuts

    PoW ID: 2991

    Geometry / Measurement, 6th to 8th, High School, Geometry, Geometry, Geometry, Geometry Library

    Problem Print

    My mom knows I like geometry, so when she saw these hexagonal cake pans, she knew she had to get them for my birthday. I'm going to use the pans to make four gingerbread cakes this weekend. I won't put any icing on the cakes, but will make some whipped cream that my friends can help themselves to.

    Five friends and I are going to cut one of the cakes into six congruent pieces. We can do this by making three straight cuts that connect opposite vertices of the hexagon and cross in the center. This gives us six congruent equilateral triangles.

    We'd like to split each of the remaining three cakes into six congruent pieces. However, we don't want to cut any two cakes in the same way. Figure out and describe how we could cut each of the remaining cakes.

    Answer Check

    Show Answer

    There are many solutions to this problem. Here are two possibilities:

    Be sure that you have included a good description of your methods or have included a picture.

    Now review your work:

    • Have you included three different methods?
    • Are the pieces created by each method congruent?
    • If you haven't included a picture, have you described each method clearly enough that another student could generate the picture for you?
    • Are there any hints that you would give another student?

    Revise your work if you have any ideas to add. Otherwise leave us a comment that tells us how you think you did - you might answer one or more of the questions above.