It is possible to know the area of a polygon only by knowing his edges and angles ?

FastChef
FastChef

And if not, why ?

Thanks.

All urls found in this thread:
https://en.wikipedia.org/wiki/Planimeter
https://en.wikipedia.org/wiki/Shoelace_formula
viagrandad
viagrandad

@FastChef
of course. the angles and side lengths of a polygon completely define it. Here's an exercise as a sort of proof: Can you change the area of a polygon without changing the sidelengths or the angles?

massdebater
massdebater

@FastChef
Did you just assume the gender of that polygon?

Carnalpleasure
Carnalpleasure

@massdebater
Someone permaban this /pol/ cancer.

Emberfire
Emberfire

@massdebater
It is not a particular polygon.

RavySnake
RavySnake

@viagrandad
Here's an exercise as a sort of proof
Nope assuming the number of side is the same.

VisualMaster
VisualMaster

No.

Well, it depends. Most of the time no. If you gave me a polygon with some parallel sides maybe. It's area would have to be defined in terms of its side which comprises itself in varying magnitudes in the other sides the most methinks.

Harmless_Venom
Harmless_Venom

@FastChef
Yes. Your question is inverse-equivalent to asking : "Are there two polygons with the same angles&edges with different areas?" which is obviously not true.

New_Cliche
New_Cliche

@FastChef

Yes. Divide the polygon into triangles. The area of any one triangle is:

A = a x b x sin (alpha) / 2, where a and b are the length of any two sides and alpha is the angle between them.

If you have any triangles without already known parameters, you can use basic geometry and the laws of sins and cosines to find them.

JunkTop
JunkTop

@massdebater
keked and checked

GoogleCat
GoogleCat

Nad if not, why ?

Nahkts.

Boy_vs_Girl
Boy_vs_Girl

@FastChef
This field is called computational geometry. Textbooks exist and contain the answers to your questions.

Crazy_Nice
Crazy_Nice

Ok thanks for replies.

SomethingNew
SomethingNew

@Harmless_Venom
Not so obvious to me.

Methshot
Methshot

@FastChef
yes. you could turn the whole thing into triangles and there's a formula for that. if it was just the angles you couldn't solve.

Sharpcharm
Sharpcharm

@massdebater
miles please stop shitposting on Veeky Forums

VisualMaster
VisualMaster

@massdebater
I mean it has phallic features

Boy_vs_Girl
Boy_vs_Girl

@SomethingNew
Polygons are uniquely defined by their points, if you know all angles and edges you know all the points.

MPmaster
MPmaster

@FastChef
Sure, it's easy by employing the chemist's integral.
Just draw the polygon on a piece of paper, cut it out and weigh it.

Soft_member
Soft_member

@FastChef
All angles and atleast 1 edge that should suffice

TechHater
TechHater

@FastChef
if you don't have vertices then you can calculate them from the edges
than you can triangulate the polygon
than you get the sum of all triangle areas

Raving_Cute
Raving_Cute

@VisualMaster
if you know the lengths and angles then you can calculate all the triangles that comprise that shape.

Evil_kitten
Evil_kitten

@FastChef
No
you need atleast one leanght

double all sides and you have another polygon with the same angles

Burnblaze
Burnblaze

@Evil_kitten
that's what OP means with edges I guess.
Also you need more than one length if you're not just discribing a triangle.
consider the a polygon with 4 90° angles and one sidelength given. There's an infinite number of rectangles that fit into that discription.

5mileys
5mileys

@FastChef
Isnt this literally what line integrals are for? Green's theorem?

askme
askme

@Raving_Cute
Or just trace it

https://en.wikipedia.org/wiki/Planimeter

Ignoramus
Ignoramus

triangulation or green's theorem

Supergrass
Supergrass

@FastChef
@massdebater
kek

PurpleCharger
PurpleCharger

@5mileys
this. fix one point at (0,0), the next at (L,0) where L is the length of the first edge. Go around to figure out the (x,y) coordinates of the other points. Then use a special case of green's theorem, i.e.

https://en.wikipedia.org/wiki/Shoelace_formula

WebTool
WebTool

@Sharpcharm
Racism belongs on /pol/

Booteefool
Booteefool

@Soft_member
No, pic related is a counter example. All angles are the same, but only one edge has changed.

Harmless_Venom
Harmless_Venom

@Booteefool
*three edges

Point is the same though.

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