View source for Analytically irreducible ring

This article gives some formulae of some [[shape]]s, using words rather than symbols.

==2-dimensional space==

===[[Perimeter]]===

====[[Circle]]/spherical [[digon]]/spherical [[henagon]]====
:Perimeter = [[π]] × [[diameter]].

====[[Polygon]]s====
:Perimeter = The sum of the lengths of the sides.

===[[Area]]===

====[[Circle]]/spherical [[digon]]/spherical [[henagon]]====
:Area = π × [[radius]]<sup>2</sup>

====[[Ellipse]]====
:Area = Half of short axis × half of long axis × [[π]]

====[[Triangle]]====

=====[[Equilateral triangle]]=====

:Area = <math>\sqrt{3}</math> × side<sup>2</sup> ÷ 4

=====[[right-angled triangle|Right-angled]]=====
:Area = One leg × the other leg ÷ 2

=====General=====
:Area = Base × height ÷ 2
:Numerous other formulas are given [[Triangle#Computing the area of a triangle|here]]

====[[Quadrilateral]]====

=====[[Square]]=====
:Area = Side<sup>2</sup>

=====[[Rectangle]]=====
:Area = One side × the other side

=====[[Parallelogram]]=====

:Area = One side × height from that side

=====[[Trapezoid]]=====

:Area = Sum of the lengths of the parallel sides × height between the parallel sides ÷ 2

=====[[Kite]] or other [[Orthodiagonal quadrilateral|quadrilateral with perpendicular diagonals]]=====

:Area = One diagonal × the other diagonal ÷ 2

=====[[Bicentric quadrilateral]] (with both an [[incircle]] and a [[circumcircle]])=====

:Area = Square root of the product of the four sides

====[[Regular polygon]]====

:Area = Perimeter × distance from the center to a side ÷ 2

==3-dimensional space==

===[[Surface area]]===

====[[Sphere]]====
:Surface area = 4 × radius<sup>2</sup> × π

====[[Cone]]====

:Surface area = π × (radius of base)<sup>2</sup> + π × (radius of base) × height of cone

====[[Cylinder (geometry)|Cylinder]]====
:Surface area = 2 × π × radius × height + 2 × π × radius<sup>2</sup>

====Regular [[tetrahedron]]====
:Surface area = <math>\sqrt{3}</math> × (edge length)<sup>2</sup>

====Square-based pyramid====
:Surface area = (Side of base)<sup>2</sup> + 2 × (side of base) × [[slant height]]

====[[Cube]]====
:Surface area = (Side)<sup>2</sup> × 6

====Regular [[octahedron]]====
:Surface area = 2 × <math>\sqrt{3}</math> × (edge length)<sup>2</sup>

===[[Volume]]===

====[[Sphere]]====
:Volume = {{frac|4|3}} × π × radius<sup>3</sup>

====[[Cone]]====
:Volume = {{frac|1|3}} × π × (radius of base)<sup>2</sup> × height

====[[Cylinder]]====
:Volume = π × radius<sup>2</sup> × height

====[[Cube]]====
:Volume = Side<sup>3</sup>

====Regular [[cuboid]]====
:Volume = The product of the three sides

==4-dimensional space==

===[[Hypervolume]]===

====[[Tesseract]]====
:Hypervolume = Side<sup>4</sup>

==References==
*''More Murderous'' Maths by Kjartan Poskitt
*''Algebra And Geometry'' by Dan Green and Basher



[[Category:Size]]