Fun Geometry Question:
If given the following 5-sided polygon with area A units squared, can you find a 3-sided polygon having the same area by messing with the given polygon?

Question

myininaya · Answer

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zarkon · Answer

do I give away the answer...or just wait for someone else to figure it out :)

myininaya · Answer

If you want someone else to discover it, then I guess we wait.

myininaya · Answer

I had to play a little with it, but it looks like we  can do the same process for any convex n-gon to any convex (n-k)-gon.

zarkon · Answer

sure...by induction...this being the basis step (or one vertex more than the basis step)

zarkon · Answer

Hopefully a student will drop in and try it. :)

amistre64 · Answer

im kinda wondering what "messing with the given polygon" might be defined as.  I tried yelling at it, but not too sure if that worked :)

myininaya · Answer

Well what was the reaction?

amistre64 · Answer

it recoiled in horror and confessed to being a three sided equi-areal assessment.  I then gave it a cookie and we watched NCIS together, but on mute.

myininaya · Answer

Yep, it wasn't suppose to react that way to that kinda messing.

amistre64 · Answer

kids these days, they just cant be trusted lol

myininaya · Answer

Is the polygon a kid, now?

amistre64 · Answer

it might as well be .... if it sits there and argues with you and spews lies at every given moment, then it has to be a kid that spends all day sitting on the couch eating the chicken potpies straight out of the freezer.

amistre64 · Answer

did i mention, my daughter is living with me now?  ;)

myininaya · Answer

So you have a polygon living with you?

myininaya · Answer

Just remember you cannot enter into a polygon. There is no opening. You can not hop into it.

amistre64 · Answer

a 3 sided polygon that is disguising itself as a 5 sided poly of indeterminable area.  We are in flatland right?

myininaya · Answer

Yes.

amistre64 · Answer

all these polys look the same to me :)

ganeshie8 · Answer

straight lines

ganeshie8 · Answer

guess i found a method, il wait for others to try proly

amistre64 · Answer

my method is patent pending .. so no stealing it!!

myininaya · Answer

What kinda straight lines are you talking about exactly?

ganeshie8 · Answer

was saying in amistre's flatland its all straight lines he sees.. he may not even see polys :)

solution looks too simple after letting it settle in my head a bit... its just to do with making few constructions to straighten up multiple sides.

myininaya · Answer

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