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