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

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

@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

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

Carnalpleasure

@massdebater
Someone permaban this /pol/ cancer.

Emberfire

@massdebater
It is not a particular polygon.

RavySnake

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

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

@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

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

@massdebater
keked and checked

Nahkts.

Boy_vs_Girl

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

Crazy_Nice

Ok thanks for replies.

SomethingNew

@Harmless_Venom
Not so obvious to me.

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

@massdebater
miles please stop shitposting on Veeky Forums

VisualMaster

@massdebater
I mean it has phallic features

Boy_vs_Girl

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

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

@FastChef
All angles and atleast 1 edge that should suffice

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

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

Evil_kitten

@FastChef
No
you need atleast one leanght

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

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

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

@Raving_Cute
Or just trace it

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

Ignoramus

triangulation or green's theorem

Supergrass
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

@Sharpcharm
Racism belongs on /pol/

Booteefool

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

Harmless_Venom

@Booteefool
*three edges

Point is the same though.