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Geometry

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Polygons Side-Length Ratio to Diameter
Units of Size
Areas of Polygons
Angles Sizes Sum in Polygons
Quadrilaterals Types Equations
Triangles Equation
Pentagon Angles
Hexagon
Circle Equations

Polygons

Polygon means many sides when translated from some language (I think the language is Greek). Polygons that have all their segments (lines) the same distance and have all their inner angles the same are called regular polygons. The diameter for each of these is 1.
Number of Sides
Name
Picture
Length of each side
1 Point
1
0
2 Segment
2
1
3 Triangle
3
√(3)/2 = .8660
4 Quadrilateral
4
√(2)/2 = .7071
5 Pentagon
5
√(-2*(√(5)-5))/4 = .5878
6 Hexagon
6
1/2 = .5000
7 Heptagon
7
 = .4339
8 Octagon
8
√(2-√(2))/2 = .3827
9 Nonagon
9
 = .3420
10 Decagon
10
√(-2*(√(5)-3))/4 = .3090
11 Undecagon
11
 = .1318 Err
12 Dodecagon
12
√(2-√(3))/2 = .1262 Err
16 Hexadecagon
16
√(2-√(2+√(2)))/2 = .1951
20 (-2*(√(2*(5+√(5)))-4))/4 = .0977 Err
24 Icosikaitera
24
√(-2*(√(6)+√(2)-4))/4 = .0892 Err
30
32 √(2-√(2+√(2+√(2))))/2 = .0980
60
100
120
360
720
∞ circle 0
n SQRT((1-cos(360/n))/2)
sin(360/(2*x)) = √((1-cos(360/x))/2)
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Units of Size


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Areas of Polygons


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Angles


If n = the number of sides in a polygon, then (n-2)*180 = the sum of all the inner angles in the polygon.
Number of Sides
Sum of Angles
Sum of Angles/Number of Sides=average of each angle
0 -360 infinity
1 -180 -180
2 0 0
3 180 60
4 360 90
5 540 108
6 720 120
7 900 900/7≈128.571428571428
8 1080 135
9 1260 140
10 1440 144
11 1620 1620/11≈147.27272727
12 1800 150
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Quadrilaterals

There are a few types of quadrilaterals. A quadrilateral is any polygon which has only four sides. A trapazoid is any quadrilateral which has no parallel lines. A parallelogram is any quadrilateral which has two sets of parallel lines. A rhombus (not a diamond) is any parallelogram which has all of its sides the same length. A rectangle is any parallelogram which has all angles the same. Therefore the only angle that could be used is a 90 degree angle. A square is any parallelogram which has all of its sides the same length and all of its angles the same angle.

Quadrilateral Equation of Circumference Equation of Area Picture
Square 4*s s2
Rectangle 2*(s1+s2) s1*s2
Rhombus 2*(s1+s2)
Parallelogram 2*(s1+s2)
Trapazoid s1+s2+s3+s4
Quadrilateral s1+s2+s3+s4

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Triangles

For any triangle, A=h*b/2, Area=height*base/2
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Pentagon


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Hexagon


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Circle

d=2r
r=d/2
C=πd
A=πr2
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Posted By: Floyd     Page Posted: Home Page/Mathematics Portal/Geometry     Time/Date Posted: 2023-12-13-14-19-21     Length of Message: 46
trapezoid must have one pair of parallel lines

Posted By: Floyd     Page Posted: Home Page/Mathematics Portal/Geometry     Time/Date Posted: 2023-12-13-14-14-43     Length of Message: 78
There is some confusion between "length of side" and x value in list of shapes

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