1D Line , Circular Arc , Parabola , Helix , Koch Curve
2D
Regular Polygons: Equilateral Triangle , Square , Pentagon , Hexagon , Heptagon , Octagon , Nonagon , Decagon , Hendecagon , Dodecagon , Hexadecagon , N-gon , Polygon Ring
Other Polygons: Triangle , Right Triangle , Isosceles Triangle , IR Triangle , 1/2 EL Triangle , Quadrilateral , Rectangle , Golden Rectangle , Rhombus , Parallelogram , Kite , 60-90-120 Kite , Half Square Kite , Right Kite , Trapezoid , Right Trapezoid , Isosceles Trapezoid , Tri-equilateral Trapezoid , Obtuse Trapezoid , Cyclic Quadrilateral , Tangential Quadrilateral , Arrowhead , Concave Quadrilateral , Crossed Rectangle , Antiparallelogram , House-Shape , Symmetric Pentagon , Diagonally Bisected Octagon , Cut Rectangle , Concave Pentagon , Concave Regular Pentagon , Stretched Pentagon , Straight Bisected Octagon , Stretched Hexagon , Symmetric Hexagon , Semi-regular Hexagon , Parallelogon , Concave Hexagon , Arrow-Hexagon , Rectangular Hexagon , L-Shape , Sharp Kink , T-Shape , Square Heptagon , Truncated Square , Stretched Octagon , Frame , Open Frame , Grid , Cross , X-Shape , H-Shape , Threestar , Fourstar , Pentagram , Hexagram , Unicursal Hexagram , Oktagram , Star of Lakshmi , Double Star Polygon , Polygram , The Hat , Polygon
Round Forms: Circle , Semicircle , Circular Sector , Circular Segment , Circular Layer , Circular Central Segment , Round Corner , Circular Corner , Circle Tangent Arrow , Drop Shape , Crescent , Pointed Oval , Two Circles , Lancet Arch , Knoll , Annulus , Semi-Annulus , Annulus Sector , Annulus Segment , Cash , Curved Rectangle , Rounded Polygon , Rounded Rectangle , Ellipse , Semi-Ellipse , Elliptical Segment , Elliptical Sector , Elliptical Ring , Stadium , Spiral , Log. Spiral , Reuleaux Triangle , Cycloid , Double Cycloid , Astroid , Hypocycloid , Cardioid , Epicycloid , Parabolic Segment , Heart , Tricorn , Pointed Semicircle , Interarc Triangle , Circular Arc Triangle , Interarc Quadrangle , Intercircle Quadrangle , Circular Arc Quadrangle , Circular Arc Polygon , Claw , Half Yin-Yang , Arbelos , Salinon , Bulge , Lune , Three Circles , Polycircle , Round-Edged Polygon , Rose , Gear , Oval , Egg-Profile , Lemniscate , Squircle , Circular Square , Digon , Spherical Triangle
3D
Platonic Solids: Tetrahedron , Cube , Octahedron , Dodecahedron , Icosahedron
Archimedean Solids: Truncated Tetrahedron , Cuboctahedron , Truncated Cube , Truncated Octahedron , Rhombicuboctahedron , Truncated Cuboctahedron , Icosidodecahedron , Truncated Dodecahedron , Truncated Icosahedron , Snub Cube , Rhombicosidodecahedron , Truncated Icosidodecahedron , Snub Dodecahedron
Catalan Solids: Triakis Tetrahedron , Rhombic Dodecahedron , Triakis Octahedron , Tetrakis Hexahedron , Deltoidal Icositetrahedron , Hexakis Octahedron , Rhombic Triacontahedron , Triakis Icosahedron , Pentakis Dodecahedron , Pentagonal Icositetrahedron , Deltoidal Hexecontahedron , Hexakis Icosahedron , Pentagonal Hexecontahedron
Johnson Solids: Pyramids , Cupolae , Rotunda , Elongated Pyramids , Gyroelongated Pyramids , Bipyramids , Elongated Bipyramids , Gyroelongated Square Dipyramid , Gyrobifastigium , Disheptahedron , Snub Disphenoid , Sphenocorona , Disphenocingulum
Other Polyhedrons: Cuboid , Square Pillar , Triangular Pyramid , Square Pyramid , Regular Pyramid , Pyramid , Square Frustum , Regular Frustum , Frustum , Bent Pyramid , Regular Bipyramid , Bipyramid , Bifrustum , Frustum-Pyramid , Ramp , Right Wedge , Wedge , Half Tetrahedron , Rhombohedron , Parallelepiped , Regular Prism , Prism , Oblique Prism , Anticube , Antiprism , Prismatoid , Trapezohedron , Disphenoid , Corner , General Tetrahedron , Wedge-Cuboid , Half Cuboid , Skewed Cuboid , Ingot , Skewed Three-Edged Prism , Cut Cuboid , Truncated Cuboid , Obtuse Edged Cuboid , Elongated Dodecahedron , Truncated Rhombohedron , Obelisk , Bent Cuboid , Hollow Cuboid , Hollow Pyramid , Hollow Frustum , Star Pyramid , Stellated Octahedron , Small Stellated Dodecahedron , Great Stellated Dodecahedron , Great Dodecahedron , Great Icosahedron
Round Forms: Sphere , Hemisphere , Spherical Corner , Cylinder , Cut Cylinder , Oblique Cylinder , Bent Cylinder , Elliptic Cylinder , Generalized Cylinder , Cone , Truncated Cone , Oblique Circular Cone , Elliptic Cone , Truncated Elliptic Cone , General Cone , General Truncated Cone , Bicone , Truncated Bicone , Pointed Pillar , Rounded Cone , Drop , Spheroid , Ellipsoid , Semi-Ellipsoid , Spherical Sector , Spherical Cap , Spherical Segment , Spherical Central Segment , Double Calotte , Double Sphere , Spherical Wedge , Half Cylinder , Diagonally Halved Cylinder , Cylindrical Wedge , Cylindrical Sector , Cylindrical Segment , Flat End Cylinder , Half Cone , Conical Sector , Conical Wedge , Spherical Shell , Half Spherical Shell , Spherical Shell Cap , Cylindrical Shell , Cut Cylindrical Shell , Oblique Cylindrical Shell , Hollow Cone , Truncated Hollow Cone , Spherical Ring , Torus , Spindle Torus , Toroid , Torus Sector , Toroid Sector , Arch , Reuleaux-Tetrahedron , Capsule , Capsule Segment , Double Point , Anticone , Truncated Anticone , Sphere-Cylinder , Lens , Concave Lens , Barrel , Egg Shape , Paraboloid , Hyperboloid , Oloid , Steinmetz Solids , Solid of Revolution
4D
Tesseract , Hypersphere
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Polygon Calculator
Calculations at a simple polygon. A polygon consists of straight edges and at least three vertices. It is simple when the edges don't intersect, so if the polygon isn't crossed . Here the edge lengths as well as the perimeter and area of the polygon can be calculated from the cartesian coordinates. First enter the number of vertices (3 to 30), then the x- and y-coordinate of each vertex. Choose the number of decimal places, then click Calculate. Side 1 runs from vertex 1 to vertex 2, side 2 from vertex 2 to 3, ..., the last side runs from vertex n to 1.

Polygon shape. If this polygon is drawn crossed, then the upper area calculation is incorrect:

Formulas:
Length of edge i = √

( x_{i+1} - x_{i} )² + ( y_{i+1} - y_{i} )²
n
p = Σ √ ( x_{i+1} - x_{i} )² + ( y_{i+1} - y_{i} )²
i=1

n
A = | Σ x_{i} * y_{i+1} - y_{i} * x_{i+1} | / 2
i=1

with x_{n+1} → x_{1} and y_{n+1} → y_{1}
Σ is the

sum symbol , | | is the absolute value.

x- and y-coordinate determine the position of a point right from and above the origin in the cartesian coordinate system. Edge lengths and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

The calculation of the simple polygon is done using the Gaussian trapezoid formula, which was discovered by Carl Friedrich Gauss and Carl Gustav Jacob Jacobi in the 19th century. This formula assigns a trapezoid to each edge of the polygon. These trapezoids have positive or negative areas, depending on whether they are inside or outside the polygon. Finally, all of these areas are added together to obtain the area of the simple polygon. The perimeter is calculated in a similar way, only with the edge lengths instead of the areas.
The input is cumbersome, but any polygon can be calculated with this. For polygons with a specific shape, for which there are separate formulas and calculators, especially for triangles and quadrilaterals , these are definitely preferable.

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