Difference between revisions of "Square (geometry)"

Latest revision as of 16:11, 21 July 2025

A square is a quadrilateral in which all sides have equal length and all angles are right angles.

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

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. $D=\sqrt{s^2+s^2}=s\sqrt{2}$

You can also find the area of a square using its diagonal. ${D^2}/2$ is equivalent to the area of a square.

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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>
+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.
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