Copyright © University of Cambridge. All rights reserved.

## 'Lying and Cheating' printed from http://nrich.maths.org/

Follow the instructions and you can take a rectangle, cut it
into 4 pieces, discard two small triangles, put together the
remaining two pieces and end up with a rectangle the same size. Try
it! Clearly there is something wrong here but can you explain what
it is?

- - =

Take some squared paper and cut out a rectangle 10 units by 11
units.As shown in the diagram, cut along the diagonal and cut off
the two red triangles, each of which has a side of length one unit.
Put the two red triangles to one side.

Now slide the right hand piece down (moving one edge that had
been the diagonal along the other) until you make another
rectangle. The top edge of the new rectangle is 10 units long but
the left hand edge becomes 11 units. Thus the new rectangle is the
same as the one you started with. (11 units by 10 units).