## Challenge: Finding the midline of an irregular shape

Geometric formulae, word problems, theorems and proofs, etc.
MattRNR
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Joined: Sat Apr 30, 2016 9:36 am
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### Challenge: Finding the midline of an irregular shape

G’day purple math

I find myself grappling with something of a geometric noodle scratcher and was hoping someone might be able to render some assistance, advice or even a solution.

I’m working with 2 irregular shapes (Area’s B and C, representing two potential configurations for the exercise yards of a kennel) and attempting to identify the position of the horizontal lines (as measured from the lower left corner of the shape up the left boundary) that divide each shape (A, B and C) such that the portion of that shape above the line equates to the portion below (please see diagrams as I am truly shocking at explaining this).

http://speedy.sh/fDVcN/1.png

Please note; A) I couldn't work out how to upload a picture so I used speedyshare and B) I drastically over calculated Area B in the above diagram, it should equal 2997.63m2

http://speedy.sh/9Pg5f/2.png
http://speedy.sh/d7RQw/3.png
http://speedy.sh/bKJnE/4.png

The measurements are not perfect so I’m really trying to work out just how to do it at this stage. I’m usually not too bad at this kind of stuff so it’s immensely frustrating that I can’t see how to work it out, it seems deceptively simple to me.

The only notion I can think of is to use the hypothetical triangle that would exist were the sides of the area extended, find some way of dividing it horizontally and then use the area of the non-existent parts of the hypothetical triangle to adjust the position of the mid line (using the difference between value 1 (V1) and value 2 (V2), again please see diagram and forgive my scribbling).

http://speedy.sh/CMcPg/5.jpg

Is there any mathematical validity in this kind of approach? Or am I just delusional from sleep deprivation…

Any thoughts on how to find these figures would be greatly appreciated.

Regards
MattRNR

little_dragon
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Joined: Mon Dec 08, 2008 5:18 pm
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