Square (geometry): Difference between revisions
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A '''square''' is [[quadrilateral]] in which all [[edge|sides]] have equal length and all [[angle | angles]] are [[right angle]]s. | A '''square''' is a [[quadrilateral]] in which all [[edge|sides]] have equal length and all [[angle | angles]] are [[right angle]]s. | ||
Equivalently, | <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. | |||
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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> | 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> | ||
You can also find the area of a square using its diagonal. <math>{D^2}/2</math> is equivalent to the area of a square. | |||
== See Also == | == See Also == | ||
* [[Unit Square]] | * [[Unit Square]] | ||
* [[Cube (geometry) | Cube]] | * [[Cube (geometry) | Cube]] | ||
[[Category:Geometry]] | |||
[[Category:Definition]] | |||
{{stub}} | |||
Latest revision as of 15:11, 21 July 2025
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. 
You can also find the area of a square using its diagonal. 
is equivalent to the area of a square.
See Also
This article is a stub. Help us out by expanding it.
