How can I dissect a triangle into 4 piece and form a square? I took A right triangle with sides 3,4,5.i was able to get a rectangle of side 3 and 2,if I dissect that I was able to get 3 squares of sides 2,1,1. I am new to dissection problems I just need to know how to approach these kind of problems


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  • $\begingroup$ Is there a more specific question you have? do you have an example picture? $\endgroup$ – Sam Harrington May 23 '17 at 17:36
  • $\begingroup$ What kind of triangle? Isosceles triangle? Right triangle? Or are you asking for a general-case solution? $\endgroup$ – MikeQ May 23 '17 at 17:56
  • $\begingroup$ It is a right triangle $\endgroup$ – swetha May 24 '17 at 15:06

Solution for a right isosceles triangle.

enter image description here

Solution for an equilateral triangle:

You can dissect it via the Dudeny Dissection. Image is from Wikipedia. enter image description here

This answer may be a partial solution. Assuming that "square" means "regular quadrilateral with equal sides", then I don't think there is a general-case solution that fits your question for all possible triangles. You may be thinking of the

Wallace–Bolyai–Gerwien theorem.

According to the theorem, any triangle can be dissected and rearranged into a square with equal area. However, it does not guarantee that it is dissected into 4 pieces.

  • $\begingroup$ Actually, it has been proved that there exists a chained - i.e where are pieces remain in a chain as in your example - disection from any convex (not sure if this is a condition) polygon to any other (convex?) polygon $\endgroup$ – Wen1now May 23 '17 at 21:19

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