Determining Areas of Triangles in Hexagon ABCDEF

In summary: So we are left with two unknowns and two equations to find them.In summary, the speaker is discussing a problem involving a hexagon with known areas of some of its triangles and a point inside. They are trying to determine the area of the remaining two triangles and considering utilizing symmetry to solve the problem. However, it is noted that the hexagon may not be a regular one, making it difficult to find the individual areas of the remaining triangles.
  • #1
Numeriprimi
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0
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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  • #2
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
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
Simon Bridge said:
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.
 
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  • #5
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.
 

1. How do you determine the area of a triangle in a hexagon?

To determine the area of a triangle in a hexagon, you can use the formula A = 1/2 * base * height, where the base is the length of one side of the triangle and the height is the perpendicular distance from the base to the opposite vertex. You can also use Heron's formula, which takes into account all three sides of the triangle.

2. Can you use the same method to find the area of any triangle in a hexagon?

Yes, the same formula can be used to find the area of any triangle in a hexagon. However, you may need to break the hexagon down into smaller triangles in order to use the formula.

3. What is the difference between a regular and irregular hexagon?

A regular hexagon has six equal sides and angles, while an irregular hexagon has sides and angles of varying lengths and sizes. This can affect the method used to determine the area of a triangle in the hexagon.

4. Can you use trigonometry to determine the area of a triangle in a hexagon?

Yes, you can use trigonometry to determine the area of a triangle in a hexagon. By using the Law of Cosines or Law of Sines, you can find the length of each side and then use the formula A = 1/2 * base * height to find the area.

5. Are there any other methods for determining the area of a triangle in a hexagon?

Yes, there are other methods for determining the area of a triangle in a hexagon. These include using the Pythagorean theorem, dividing the hexagon into smaller shapes such as rectangles or parallelograms, or using coordinates and the Shoelace formula.

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