Geometry | Forms | Contact & Privacy Geometric Calculators German: Geometrierechner, Formen

1DLine, 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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Trapezoid Calculator

Calculations at a trapezoid. A trapezoid (or trapezium) is a tetragon with two parellel sides.
Enter three side lengths and one angle between two of those sides. Choose the number of decimal places and click Calculate. Please enter angles in degrees, here you can convert angle units. Only those trapezoids can be calculated here, where c doesn't overlap a (g1, g2 ≥ 0; α, β ≤ 90°), for others see obtuse trapezoid.
Example for a trapezoid: a=4, b=3, c=2.5, β=80°


Carl Friedrich Gauss, by Gottlieb Biermann Longer base (a): Trapezoid, Trapezium
First leg (b):
Shorter base (c):
Second leg (d):
First angle (α):
Second angle (β):
Third angle (γ):
Fourth angle (δ):
Height (h):
First diagonal (e):
Second diagonal (f):
Central median (m):
First overlap (g1):
Second overlap (g2):
Perimeter (p):
Area (A):
Round to    decimal places.



Trapezoid shape:
Formulas:
α + δ = 180°
β + γ = 180°
a = c + g1 + g2
g1 = √ d² - h²
g2 = √ b² - h²
α = arccos( (g1²+d²-h²) / ( 2*g1*d ) )
β = arccos( (g2²+b²-h²) / ( 2*g2*b ) )
h = b * sin(β) = b * sin(γ) = d * sin(α) = d * sin(δ)
e = √ a² + b² - 2ab*cos(β)
f = √ a² + d² - 2ad*cos(α)
m = ( a + c ) / 2
p = a + b + c + d
A = ( a + c ) / 2 * h

Side lengths, height, diagonals and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).


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Trapezoid, perimeter and area
perimeter p, area A
Trapezoid, sides and angles
sides and angles

Trapezoid, height
height
Trapezoid, diagonals
diagonals

Trapezoid, central median
central median

A special form of trapezoid is the parallelogram, in which not just one pair, but both pairs of opposite sides are parallel to each other. Another special case is the obtuse trapezoid, which the calculator on this page cannot calculate. There are also right trapezoids, isosceles trapezoids and tri-equilateral trapezoids. The rectangle, the rhombus and the square are also trapezoids.
In old writings from the beginning of the 20th century and before, the term trapezoid was generally used for general quadrilaterals or specifically those without parallel sides. Trapezoids in the modern sense were called parallel trapezoids. This can be confusing when reading such writings these days. The name of the three-dimensional shape trapezohedron goes back to the old meaning of the word trapezoid.
The general trapezoid has no symmetries, an isosceles trapezoid has an axis of symmetry through the middle of the two parallel sides.



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