It is possible to know the area of a polygon only by knowing

>>8593664
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?

>>8593664
Did you just assume the gender of that polygon?

>>8593711
Someone permaban this /pol/ cancer.

>>8593711
It is not a particular polygon.

>>8593701
>Here's an exercise as a sort of proof
Nope assuming the number of side is the same.

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.

>>8593664
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.

>>8593664

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.

>>8593711
keked and checked

File: raie.png (20KB, 1114x662px) Image search: [Google]

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Nad if not, why ?

Nahkts.

File: brain-in-a-vat-387x400.gif (56KB, 387x400px) Image search: [Google]

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>>8593664
This field is called computational geometry. Textbooks exist and contain the answers to your questions.

Ok thanks for replies.

>>8593782
Not so obvious to me.

>>8593664
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.

>>8593711
miles please stop shitposting on /sci/

>>8593711
I mean it has phallic features

>>8594072
Polygons are uniquely defined by their points, if you know all angles and edges you know all the points.

>>8593664
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.

>>8593664
All angles and atleast 1 edge that should suffice

File: tutorial_normals07.gif (41KB, 256x256px) Image search: [Google]

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>>8593664
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

File: triangles.png (50KB, 1030x588px) Image search: [Google]

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>>8593749
if you know the lengths and angles then you can calculate all the triangles that comprise that shape.

>>8593664
No
you need atleast one leanght

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

>>8594527
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.

>>8593664
Isnt this literally what line integrals are for? Green's theorem?

>>8594512
Or just trace it

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

triangulation or green's theorem

>>8593664
>>8593711
kek

>>8595913
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

>>8594097
Racism belongs on /pol/

File: counterexample.png (39KB, 1300x662px) Image search: [Google]

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>>8594157
No, pic related is a counter example. All angles are the same, but only one edge has changed.

>>8597921
*three edges

Point is the same though.