Difference between revisions of "Square (geometry)"
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| − | A '''square''' is a | + | A '''square''' is a [[quadrilateral]] in which all [[edge|sides]] have equal length and all [[angle | angles]] are [[right angle]]s. |
| + | |||
| + | <asy> | ||
| + | import markers; | ||
| + | pair A, B, C, D; | ||
| + | |||
| + | A = (-1, 1); | ||
| + | B = (1, 1); | ||
| + | C = (1, -1); | ||
| + | D = (-1, -1); | ||
| + | |||
| + | draw(A--B--C--D--cycle); | ||
| + | draw(rightanglemark(A, B, C)); | ||
| + | draw(rightanglemark(B, C, D)); | ||
| + | draw(rightanglemark(C, D, A)); | ||
| + | draw(rightanglemark(D, A, B)); | ||
| + | draw(A--B--C--D--cycle, StickIntervalMarker(4)); | ||
| + | </asy> | ||
| + | |||
| + | Equivalently, all squares are the [[regular polygon|regular]] quadrilaterals. | ||
== Introductory == | == Introductory == | ||
| − | |||
| − | |||
=== Area === | === Area === | ||
| − | The [[area]] of a square can be found by squaring the square's side length | + | The [[area]] of a square can be found by squaring the square's side length: the area <math>A</math> of a square with side length <math>s</math> is <math> A = s^2 </math>. |
=== Perimeter === | === Perimeter === | ||
| − | The [[perimeter]] of square can be found by multiplying the square's side length by four - <math> P = 4s </math>. | + | The [[perimeter]] <math>P</math> of a square can be found by multiplying the square's side length by four - <math> P = 4s </math>. |
=== Diagonal === | === Diagonal === | ||
| − | The [[ | + | The length of either [[diagonal]] of a square can be obtained by the [[Pythagorean Theorem | Pythagorean theorem]]. <math>D=\sqrt{s^2+s^2}=s\sqrt{2}</math> |
| + | |||
== See Also == | == See Also == | ||
| − | |||
* [[Unit Square]] | * [[Unit Square]] | ||
| − | * [[Cube]] | + | * [[Cube (geometry) | Cube]] |
| + | |||
| + | [[Category:Geometry]] | ||
| + | |||
| + | [[Category:Definition]] | ||
| + | |||
| + | {{stub}} | ||
Latest revision as of 17:31, 3 September 2024
A square is a quadrilateral in which all sides have equal length and all angles are right angles.
![[asy] import markers; pair A, B, C, D; A = (-1, 1); B = (1, 1); C = (1, -1); D = (-1, -1); draw(A--B--C--D--cycle); draw(rightanglemark(A, B, C)); draw(rightanglemark(B, C, D)); draw(rightanglemark(C, D, A)); draw(rightanglemark(D, A, B)); draw(A--B--C--D--cycle, StickIntervalMarker(4)); [/asy]](http://latex.artofproblemsolving.com/b/0/9/b099e8fd521b2fcda4322d23b57eb040ea4a5bf4.png)
Equivalently, all squares are the regular quadrilaterals.
Introductory
Area
The area of a square can be found by squaring the square's side length: the area 
of a square with side length 
is 
.
Perimeter
The perimeter 
of a square can be found by multiplying the square's side length by four - 
.
Diagonal
The length of either diagonal of a square can be obtained by the Pythagorean theorem. 
See Also
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