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Cutting Corners

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

Square to L

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.

Midpoint Triangle

Can you cut up a square in the way shown and make the pieces into a triangle?

Cut and Make

Age 7 to 11
Challenge Level

Thank you to Meg for sending us these great diagrams! Did you make the shapes in the same way?

Here is a diagram showing how the original square should be cut.

Square solution

These pieces can be arranged to make a triangle like this:
Triangle solution
The parallelogram can be made like this:
Parallelogram solution
The square can be made as shown in the first diagram.

Well done Meg!

From Class 2GW, at the Bavarian International School, the teacher sent in the following:  

They really enjoyed the Cut and Make activity this week. Although the challenge was to make a triangle, parallelogram and square, after a few minutes Jack discovered that you could make a trapezium with the three triangles. A bit later Ella discovered that she could make a rectangle. They were excited when they discovered that these weren't included in the solutions so far.
As an extra challenge, we tried to make a kite. Zoe discovered that you could only make one if you didn't cut the original square. Instead, she used the first diagonal fold line to fold in the other two corners too. So it became more of an origami kite. 


Thank you for that excellent work BIS. Why not try some more of the challenges?

If you enjoyed this puzzle, you might like to look at some of the Tangram puzzles on this site, for example Tangram or Tangrams - World of Tan.