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'Halving the Triangle' printed from http://nrich.maths.org/

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  • Draw any triangle P, Q, R.
  • Find points A, B and C, one on each side of the triangle (but not at the vertices), such that the area of triangle ABC is one quarter the area of triangle PQR.
Two triangles
  • Now find points such that the area of triangle ABC is one half the area of triangle PQR and a method that will give any fraction of the area between one quarter and one.
  • How would you adapt your method to give fractions less than one quarter?