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?
Click here to download the DOESN’T ADD UP worksheet.
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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.
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This problem was quite challenging to the learners, but after some guidance they started to understant it.