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'Fraction Fascination' printed from http://nrich.maths.org/
I drew this picture by drawing a line from the top right corner of a square to the midpoint of each of the opposite sides. Then I joined these two midpoints with another line.
Can you see four triangles in the square?
What fraction of the area of the square is each of these triangles?
Then I drew another picture:
How is this made using the first square?
What is the shape that has been created in the middle of this larger square?
What fraction of the total area of the large square does this shape take up?