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Triangles in hexagon

by Numeriprimi
Tags: hexagon, point, triangle
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Numeriprimi
#1
Jan12-13, 07:05 PM
P: 138
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
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Simon Bridge
#2
Jan12-13, 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?
Numeriprimi
#3
Jan13-13, 02:55 AM
P: 138
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?

HallsofIvy
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Jan13-13, 06:17 PM
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Triangles in hexagon

Quote Quote by Simon Bridge View Post
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?
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.
Simon Bridge
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Jan14-13, 09:44 PM
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The problem, as stated, does not suggest that this is a "regular" hexagon and so does not imply any "symmetry".
That's a good point... though the question would seem somewhat unfair if it were not.


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