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'Tilting Triangles' printed from http://nrich.maths.org/
A right-angled isosceles triangle whose two equal sides are 2
units in length is attached at its right-angled vertex to the
centre of a square of side 2 units and rotated about this centre
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What can you say about the area of the part of the square
covered by the triangle as it rotates?
What happens to this area if the triangle is reduced in size so
that its two equal sides are $ \sqrt 2 $ units?
What happens if the triangle is further reduced in size?