Look at this square divided into four pieces : two identical triangles and two identical trapezia.

The edge of length 3 from each triangle matches with the edge of length 3 from a trapezium so that the four pieces from the square now occupy a rectangular space.

The square had side length 8 and area 64.

The area of the rectangle is 65, that is 13 by 5 square units.  Can the area have changed?

Can you explain what has happened?

AIMSSEC Notes for Teachers – Doesn’t Add Up

This problem is adapted from the NRICH task Doesn’t Add Up with permission of the University of Cambridge. All rights reserved.

One Response to Grades 7 to 10 – Doesn’t Add Up

  1. Avatar Tau Tamako says:

    This problem was quite challenging to the learners, but after some guidance they started to understant it.

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