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, the 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 a 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]] |
Latest revision as of 01:12, 13 June 2022
A square is a quadrilateral in which all sides have equal length and all angles are right angles.
Equivalently, the 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.