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Square (geometry)

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


See Also

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