If u mean polygon then,
What is a Polygon?
A closed plane figure made up of several line segments that are joined together. The sides do not cross each other. Exactly two sides meet at every vertex.
Types of Polygons
Regular - all angles are equal and all sides are the same length. Regular polygons are both equiangular and equilateral.
Equiangular - all angles are equal.
Equilateral - all sides are the same length.
Convex - a straight line drawn through a convex polygon crosses at most two sides. Every interior angle is less than 180°.
Concave - you can draw at least one straight line through a concave polygon that crosses more than two sides. At least one interior angle is more than 180°.
Polygon Formulas
(N = # of sides and S = length from center to a corner)
Area of a regular polygon = (1/2) N sin(360°/N) S2
Sum of the interior angles of a polygon = (N - 2) x 180°
The number of diagonals in a polygon = 1/2 N(N-3)
The number of triangles (when you draw all the diagonals from one vertex) in a polygon = (N - 2)
Polygon Parts,
Side - one of the line segments that make up the polygon.
Vertex - point where two sides meet. Two or more of these points are called vertices.
Diagonal - a line connecting two vertices that isn't a side.
Interior Angle - Angle formed by two adjacent sides inside the polygon.
Exterior Angle - Angle formed by two adjacent sides outside the polygon.
Special Polygons,
Special Quadrilaterals - square, rhombus, parallelogram, rectangle, and the trapezoid.
Special Triangles - right, equilateral, isosceles, scalene, acute, obtuse.
Polygon Names,
Generally accepted names.
Sides Name
n N-gon
3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
7 Heptagon
8 Octagon
10 Decagon
12 Dodecagon
Names for other polygons have been proposed,
Sides Name
9 Nonagon, Enneagon
11 Undecagon, Hendecagon
13 Tridecagon, Triskaidecagon
14 Tetradecagon, Tetrakaidecagon
15 Pentadecagon, Pentakaidecagon
16 Hexadecagon, Hexakaidecagon
17 Heptadecagon, Heptakaidecagon
18 Octadecagon, Octakaidecagon
19 Enneadecagon, Enneakaidecagon
20 Icosagon
30 Triacontagon
40 Tetracontagon
50 Pentacontagon
60 Hexacontagon
70 Heptacontagon
80 Octacontagon
90 Enneacontagon
100 Hectogon, Hecatontagon
1,000 Chiliagon
10,000 Myriagon
To construct a name, combine the prefix+suffix,
Sides Prefix Sides Suffix
20 Icosikai... +1...henagon
30 Triacontakai... +2...digon
40 Tetracontakai... +3...trigon
50 Pentacontakai... + +4...tetragon
60 Hexacontakai... +5...pentagon
70 Heptacontakai... +6...hexagon
80 Octacontakai... +7...heptagon
90 Enneacontakai... +8...octagon
+9...eneagon
Examples:
46 sided polygon - Tetracontakaihexagon
28 sided polygon - Icosikaioctagon
However, many people use the form n-gon, as in 46-gon, or 28-gon instead of these names.
I think i have helped u,
& if u mean pentagon then,
A pentagon is a five-sided polygon. Commonly, the term "pentagon" is used to refer to the regular pentagon.
The regular pentagon is the regular polygon with five sides.
A number of distance relationships between vertices of the pentagon can be derived by similar triangles
d/1=1/1/fi=fi
where is the diagonal distance.But the dashed vertical line connecting two nonadjacent polygon vertices is the same length as the diagonal one, so
fi=1+1/fi
fi*2-fi-1
Solving the quadratic equation and taking the plus sign (since the distance must be positive) gives the golden ratio
fi=1/2(1+underroot 5)
The coordinates of the vertices of a regular pentagon inscribed in a unit circle relative to the center of the pentagon are
c1=cos(2 pi/5)=1/4(underroot 5-1)
c2=cos(pi/5)=1/4(underroot5+1)
s1=sin(2 pi/5)=1/4 whole undrroot of(10+2 underroot5)
s2=sin(4 pi/5)=1/4 whole undrroot of(10-2 underroot5)
These points are located at every edge of pentagon such as;
(c1,s1)(1,0)(c1,-s1)(-c2,-s2)(-c2,s2)
The circumradius, inradius, sagitta, and area of a regular pentagon of side length alpha are given by;
R=1/10 @ whole root of(50+10 root 5)
r=1/10 @ whole root of(25+10 root 5)
x=1/10 @ whole root of(25-10 root 5)
A=1/4 @*2 whole root of(25+10 root 5)
where @=alpha.
Five pentagons can be arranged around an identical pentagon to form the first iteration of the "pentaflake," which itself has the shape of a pentagon with five triangular wedges removed. For a pentagon of side length 1, the first ring of pentagons has centers at radius fi , the second ring at fi cube , and the th at fi to the power 2x-1.
In proposition IV.11, Euclid showed how to inscribe a regular pentagon in a circle. Ptolemy also gave a ruler and compass construction for the pentagon in his epoch-making work The Almagest. While Ptolemy's construction has a simplicity of 16, a geometric construction using Carlyle circles can be made with geometrography symbol , which has simplicity 15 (De Temple 1991).
The following elegant construction for the pentagon is due to Richmond (1893). Given a point, a circle may be constructed of any desired radius, and a diameter drawn through the center. Call the center O, and the right end of the diameter P1 . The diameter perpendicular to the original diameter may be constructed by finding the perpendicular bisector. Call the upper endpoint of this perpendicular diameter B. For the pentagon, find the midpoint of OB and call it D. Draw DP1, and bisect angleODP1 , calling the intersection point withOP1N2 . Draw N2P2 parallel to OB , and the first two points of the pentagon are P1 and P2 , and copying the angle P1OP2 then gives the remaining points P3P4P5, , and (Coxeter 1969, Wells 1991).
Madachy (1979) illustrates how to construct a pentagon by folding and knotting a strip of paper.