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Triangles in hexagon

  1. Jan 12, 2013 #1
    I have hexagon ABCDEF (30 cm2) and point M inside.
    True: ABM = 3 cm2; BCM = 2 cm2; DEM = 7 cm2 ; FEM = 8cm2

    How can I determine area of others two triangles? I know their total area, but how individually?

    Thanks very much and if you don't understand, write, I will try to write better.
    Poor Czech Numeriprimi
  2. jcsd
  3. Jan 12, 2013 #2

    Simon Bridge

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    You exploit the symmetry of the hexagon ... did you sketch it out?
    Point M is closest to B and C, closer to B than C - right?

    Can you find the length of the line segments radiating from M in terms of the areas you know?
  4. Jan 13, 2013 #3
    How can I exploit symmetry?
    And yes, it is right, but but what good is it useful?
    I don't understand your third question.... What length from M?
  5. Jan 13, 2013 #4


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    The problem, as stated, does not suggest that this is a "regular" hexagon and so does not imply any "symmetry".

    Numeri Primi, it is easy, as you say, to see that the total area of the two remaining triangles is 30- (3+ 2+ 7+ 8)= 30- 20= 10. But there is NO way to determine the area of the two triangles separately. It is possible to construct many different (non-symmetric) hexagons having the given information but different areas for the last two triangles.
    Last edited by a moderator: Jan 14, 2013
  6. Jan 14, 2013 #5

    Simon Bridge

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    That's a good point... though the question would seem somewhat unfair if it were not.
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