Difference between revisions of "Square (geometry)"

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.

$[asy] import markers; pair A, B, C, D; A = (-1, 1); B = (1, 1); C = (1, -1); D = (-1, -1); draw(A--B--C--D--cycle); draw(rightanglemark(A, B, C)); draw(rightanglemark(B, C, D)); draw(rightanglemark(C, D, A)); draw(rightanglemark(D, A, B)); draw(A--B--C--D--cycle, StickIntervalMarker(4)); [/asy]$

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 $A$ of a square with side length $s$ is $A = s^2$ .

Perimeter

The perimeter $P$ of a square can be found by multiplying the square's side length by four - $P = 4s$ .

Diagonal

The length of either diagonal of a square can be obtained by the Pythagorean theorem. $D=\sqrt{s^2+s^2}=s\sqrt{2}$

@@ Line 1: / Line 1: @@
-== A Square ==
+A '''square''' is a [[quadrilateral]] in which all [[edge|sides]] have equal length and all [[angle | angles]] are [[right angle]]s.
-A square is a a special [[quadrilateral]] in that it is regular. A square has four equal sides and four equal angles, each angle measuring 90 degrees.
-== Area ==
+<asy>
-The [[area]] of a square can be found by squaring the square's side length - <math> A = s^2 </math>.
+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 ==
+=== Area ===
+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 ===
+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 ===
+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>
-== Perimeter ==
-The [[perimeter]] of square can be found by multiplying the square's side length by 4 - <math> P = 4s </math>.
 == See Also ==
-[[Quadrilateral]]
+* [[Unit Square]]
-[[Unit Square]]
+* [[Cube (geometry) | Cube]]
-[[Cube]]
+[[Category:Geometry]]
+[[Category:Definition]]
+{{stub}}

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