Regular Polygons: Equilateral Triangle, Square, Pentagon, Hexagon, Heptagon, Octagon, Nonagon, Decagon, Hendecagon, Dodecagon, N-gon
Other Polygons: Triangle, Right Triangle, Isosceles Triangle, IR Triangle, Quadrilateral, Rectangle, Rhombus, Parallelogram, Kite, Right Trapezoid, Isosceles Trapezoid, Trapezoid, Cyclic Quadrilateral, Tangential Quadrilateral, Arrowhead, Antiparallelogram, House-Shape, Concave Pentagon, Parallelogon, Threestar, Fourstar, Pentagram, Hexagram, Star of Lakshmi
Round Forms: Circle, Semicircle, Circular Sector, Circular Segment, Round Corner, Annulus, Annulus Sector, Ellipse, Stadium, Digon, Spherical Triangle, Reuleaux Triangle, Cycloid, Astroid, Hypocycloid, Cardioid, Parabolic Segment, Arbelos, Salinon, Lune, Oval, Three Circles, Lemniscate, Squircle
Platonic Solids: Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron
Archimedean Solids: Truncated Tetrahedron, Cuboctahedron, Truncated Cube, Truncated Octahedron, Rhombicuboctahedron, Icosidodecahedron, Truncated Dodecahedron, Truncated Icosahedron
Catalan Solids: Triakis Tetrahedron, Rhombic Dodecahedron, Tetrakis Hexahedron, Deltoidal Icositetrahedron, Rhombic Triacontahedron
Johnson Solids: Pyramids, Cupolae, Rotunda, Elongated Pyramids, Snub Disphenoid
Other Polyhedrons: Cuboid, Square Pillar, Square Pyramid, Regular Pyramid, Pyramid, Regular Frustum, Frustum, Bipyramid, Ramp, Right Wedge, Wedge, Rhombohedron, Parallelepiped, Prism, Oblique Prism, Antiprism, Trapezohedron, Disphenoid, Corner, General Tetrahedron, Truncated Rhombohedron, Stellated Octahedron, Small Stellated Dodecahedron, Great Stellated Dodecahedron
Round Forms: Sphere, Hemisphere, Cylinder, Cut Cylinder, Oblique Cylinder, Generalized Cylinder, Cone, Truncated Cone, Oblique Circular Cone, Elliptic Cone, Spheroid, Ellipsoid, Spherical Sector, Spherical Cap, Spherical Segment, Spherical Wedge, Cylindrical Wedge, Cylindrical Sector, Cylindrical Segment, Spherical Shell, Cylindrical Shell, Spherical Ring, , Reuleaux-Tetrahedron Torus, Capsule, Lens, Barrel, Paraboloid, Hyperboloid, Oloid, Steinmetz Solids
Calculations with lunes (crescents). Lunes occur, when a
circle partially eclipses another one. Enter the radiuses of the circles and the distance of their centers. Choose the number of decimal places, then click Calculate.
Δ = √ (a+b+c) * (b+c-a) * (c+a-b) * (a+b-c) / 4
A 1 = 2Δ + a² * arccos( (b²-a²-c²) / (2ac) ) - b² * arccos( (b²+c²-a²) / (2bc) )
Weisstein, Eric W.
Wolfram Web Resource.
A s = 2πa² - A 1
A 2 = 2πb² - A s
π = 3.141592653589793...
Radiuses and distance have a one-dimensional unit (e.g. meter), the areas have this unit squared (e.g. square meter).
areas of the lunes A 1 and A 2, section A s
radiuses and distance, here: a=2.8; b=3.6; c=4