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Triangles in hexagon 
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#1
Jan1213, 07:05 PM

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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
Jan1213, 08:49 PM

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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? 


#3
Jan1313, 02:55 AM

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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? 


#4
Jan1313, 06:17 PM

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Triangles in hexagon
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 (nonsymmetric) hexagons having the given information but different areas for the last two triangles. 


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