# Triangles in hexagon

by Numeriprimi
Tags: hexagon, point, triangle
 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
 Homework Sci Advisor HW Helper Thanks P: 13,033 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?
 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?
Math
Emeritus
Thanks
PF Gold
P: 39,682
Triangles in hexagon

 Quote by Simon Bridge 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.
Homework