Mathematics Stack Exchange
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Questions tagged [polygons]

For questions on polygons, a flat shape consisting of straight lines that are joined to form a closed chain or circuit

In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain or circuit.

A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments (i.e., by a closed polygonal chain). These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices (singular: vertex) or corners. An $n$-gon is a polygon with $n$ sides. The interior of the polygon is sometimes called its body. A polygon is a $2$-dimensional example of the more general polytope in any number of dimensions.

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How to calculate perimeter of Polygon with missing the length of one side?

I have following sides(PQRST) of a Polygon where PQ=13, QR=22, RS=8, ST=?, PT= 10 ... i need to find out ST? i don't have any angle i just have the shape? And for calculating perimeter i need to find out the ST length of polygon! This figure is…
Nomiluks
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How do i find the exterior angles of an L-shaped polygon?

I'm trying to review exterior angles after many years. It's my understanding that the sum of a polygon's exterior angles must equal 360°. How would you find the exterior angles in this polygon?
Noob Saibot
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Rotating and Scaling about centroid.

rotating $x' = x\cos(\text{angle}) - y\sin(\text{angle})$ $y' = x\sin(\text{angle}) + y\cos(\text{angle})$ Scaling $x' = x\cdot sx$ $y' = y\cdot sy$ but all formulas will doing about origin point. If i want to do about Centroid point. (I have…
Barbiyong
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How to find the side-length of a regular polygon given number of sides and diameter

For a program that I am writing, I need a function that takes in the number of sides, and the diameter, and will output side length. I have tried to ask my teachers, but none of them had time to figure it out. I first tried this equation, d being…
inyourface3445
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Inscribing stars in polygons with an odd number of vertices

We can create stars within polygons by picking a vertex and drawing a segment extending a certain consistent number of vertices from it. Most $2n$-gons seem to have one or two ways to make a star, e.g. the decagonal star, being segments connected…
Jrt4294967296
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Why is the term determinant used in the Shoelace formula for polygons when it isn't a square matrix?

In the Shoelace formula, the formula for the area of a polygon is $ A = \frac{1}{2} \begin{vmatrix} x_1 & x_2 & x_3 & ... & x_n & x_1\\ y_1 & y_2 & y_3 & ... & y_n & y_1\\ \end{vmatrix} $ I haven't seen this formally discussed, but I would like to…
AndroidV11
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Check if point is inside a convex polygon - I need an example for a formular

Can I find out if the location of a point is inside or outside a convex polygon with the below formular? D = (x2 - x1) * (yp - y1) - (xp - x1) * (y2 - y1) I assume when result of D > 0, the point location is outside and if D < 0, the point is inside…
taraz
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Sum of angles Extension to crossed polygons

Im trying to figure out the details of this algorithm posted here Extension to crossed polygons(Scroll down). The algorithm states that the sum of angles of any polygon can be found by the formula 180(n-2k) where n is the number of vertices and k a…
Lead Vaxeral
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Finding a point within polyshape that makes sub triangular area equally?

Example of polygon. I wonder how to find a point within $n$-sides polygonal shape that makes all sub-triangle areas equal. In an attached picture, how to find point $C$ that makes area $A_1=A_2=A_3=A_4=A_5$? Thanks. Another picture for clarifying.…
kmmm
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Exploding Connected Shapes

I have recently been tasked with creating an 'exploded' view for what amounts to a collection of shapes in a 2d coordinate plane. These shapes are all touching in some way. What I need to do is translate all of the coordinates of these shapes in…
Mark W
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Range of Interior Angles of Polygons

$\newcommand{\degree}{{^\circ}}$ Considering the method of of interior angles in surveying a traverse, what is the maximum range of any one interior angle? Also, what is the practical range of any one interior angle? In other words, what is the…
ground.clouds1
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What tool can I use to create 2D polygons which outputs list of coordinates?

I would like a free point and click type tool where I can create simple 2D polygon shapes on a grid using a Cartesian coordinate system. Ideally, the points can be dragged once created, and can snap to grid positions. Most importantly, I need the…
lepton
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how to find the length of a side of hexadecagon in relation to the radius or diameter.

is there an equation I can use to find the length of a side (L) of a regular hexadecagon (16 sided polygon) based on its radius (by which I mean the length from the center to on vertex) or its diameter (twice that... duh)? That would be really…
The Entramanure
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Polygons on a grid

I've tried multiple variations of polygons but can't find any that work. Do they exist? Is it possible to draw a polygon on a grid paper and divide it into two equal parts by a cut of the shape shown on the Figure (a)? Solve the same problem for a…
juA
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Formula to determine the number of exterior edges in multiple tiled hexagons

I'm looking for a formula which determines the number of external (that is, non-touching) edges in multiple tiled hexagons. By observation, there are 10 external edges when 2 hexagons are adjacent. There are 30 external edges in a pattern of 19…
ThomasDoe
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