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Shapes - Coggle Diagram
Shapes
Polygons
Pentagon
-Hedron, Irregular + Regular
Parameters
Length
Formula
Area
R
(L
N) / 2 = Any Regular Polygon
Volume
(R
(L
N) / 2) * D = Any Regular Polygon prism
1/6
(R
N
L
H) = Any Regular Polygon-based pyramid
L
Angles (internal and external)
a, b, c
Number of angles/sides
N
Depth
D
Internal "Radius"
R
Hexagon
Octagon
Septagon (7)?
Nonagon
Decagon
Dodecagon
Icosagon
2D
Triangles
Iscocelles
Equalateral
Right-angled
Parameters
Length
L
Height
Formula
Area
L * H / 2 = Triangle
(L^2 * square root of 3) / 4 = Equilateral triangle
Volume
L
H / 2
D = Triangular Prism
((L
W / 2)
H) / 3 = Triangular Pyramid
H
Depth
D
Angles (alpha,beta,gamma)
a, b, c
Width
W
Obtuse-angled
Acute-angled
2D
Rules
Interal angles must add up to 180*
A^2 + B^2 = C^2
Exterior angles must add up to 360*
4-Sided Polygons
Square
Parameters
Width
Formula, in order
Area
H * W = Rohmbus
H * W / 2 = Kite
H * W = Parralellogram
H^2 = Square
H * W = Rectangle
((BL + TL) * H) / 2= Trapezium
Volume (Prisms in most cases)
H
W
D = Rohmbus Prism
(H
W / 2)
D = Kite Prism
H
W
D= Parralellogram Prism
H^3 = Cube
H
W
D = Cuboid
(((BL + TL)
H) / 2)
D = Trapezium
Square-based Pyramid = See Polygons
((W
L)
H) / 3 = Rectangular-based Pyramid
W
Height
H
Dephth
D
Angles (in some cases)
a, b, c
Bottom Length & Top Length
BL, TL
Length
L
Rectange
Parralellogram
Trapezium
Kite
Rohmbus
2D
Pi-related
Cone
Frustrum
Circle
Parameters
Pi
Formula
Area
Pi * R^2 = Circle
Pi
R1
R2 = Ellipse
Volume
Base (either circle or ellipse) * D = Cylinder
Pi
R^2
H / 3 = Cone
Pi
R1^2
H1 / 3 - Pi
R2^2
H2 / 3 = Frustrum
((A(Bottom) + (4
A(Middle)) + A(Top)) / 6)
H = Kepler = Barrel
4/3
Pi
R^3 = Sphere
Hight
H
Radius
R
Depth
D
2D
Ellipse
Cylinder
Barrel
Sphere
3D
Special
Archimedian Bodies
Platonic Bodies
Kepler
Turncated and Simum