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The small square on top will be in the upper half of the divided figure. Now consider the figure formed by moving this square to become an extra square on the left of the second row, as shown.
Pile Driver
Age 11 to 14
ShortChallenge Level 
The small square on top will be in the upper half of the divided figure. Now consider the figure formed by moving this square to become an extra square on the left of the second row, as shown.
It may now be seen from the rotational symmetry of the figure that the line $PX$ splits the new figure in half- with that small square in the upper half.
Therefore the line which halves the area of the original figure cuts the edge $XY$ at $X$.
Therefore the line which halves the area of the original figure cuts the edge $XY$ at $X$.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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