And if not, why ?
And if not, why ?
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?
Did you just assume the gender of that polygon?
Someone permaban this /pol/ cancer.
It is not a particular polygon.
Here's an exercise as a sort of proof
Nope assuming the number of side is the same.
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.
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.
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.
keked and checked
Nad if not, why ?
This field is called computational geometry. Textbooks exist and contain the answers to your questions.
Ok thanks for replies.
Not so obvious to me.
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.
miles please stop shitposting on Veeky Forums
I mean it has phallic features
Polygons are uniquely defined by their points, if you know all angles and edges you know all the points.
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.
All angles and atleast 1 edge that should suffice
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
if you know the lengths and angles then you can calculate all the triangles that comprise that shape.
you need atleast one leanght
double all sides and you have another polygon with the same angles
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.
Isnt this literally what line integrals are for? Green's theorem?
triangulation or green's theorem
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.
Racism belongs on /pol/
No, pic related is a counter example. All angles are the same, but only one edge has changed.
Point is the same though.