ADVERTISEMENT

Square
Try this Drag the orange dots on each vertex
to reshape the square.
The square is probably the best known of the quadrilaterals.
It is defined as having all sides equal, and its interior angles all right angles (90°).
From this it follows that the opposite sides are also parallel.
A square is simply a specific case of a regular polygon, in this case with 4 sides.
All the facts and properties described for regular polygons apply to a square.
See Regular Polygons
Attributes
Vertex 
The vertex (plural: vertices)
is a corner of the square. Every square has four vertices.

Perimeter 
The distance around the square. All four sides are by definition the same length, so the perimeter is four times the
length of one side, or:
perimeter = 4s
where s is the length of one side. See also
Perimeter of a square.

Area 
Like most quadrilaterals, the area is the length of one side times the perpendicular height.
So in a square this is simply:
area = s^{2}
where s is the length of one side. See also Area of a square.

Diagonals 
Each diagonal of a square is the
perpendicular bisector
of the other.
That is, each cuts the other into two equal parts, and they cross and right angles (90°).
The length of each diagonal is
s√2
where s is the length of any one side.
For more on this see Diagonals of a square

A square can be thought of as a special case of other quadrilaterals, for example
Square inscribed in a circle
Like all regular polygons, a square can be inscribed in a circle, where each vertex is on the circle.
For more see
Inscribed square.
Calculator
Use the calculator on the right to calculate the properties of a square.
Enter any one value and the other three will be calculated. For example, enter the side length and the area will be calculated.
Similarly, if you enter the area, the side length needed to get that area will be calculated.
Constructing a square
A square can be constructed using a compass and straightedge. See
Constructing a square with compass and straightedge for an animated demonstration.
Coordinate Geometry
If you know the
coordinates
of the
vertices
of a square, you can calculate all the other properties.
For more on this, see
Square (Coordinate geometry)
Related polygon topics
General
Types of polygon
Area of various polygon types
Perimeter of various polygon types
Angles associated with polygons
Named polygons
(C) 2009 Copyright Math Open Reference. All rights reserved

COMMON CORE
Math Open Reference now has a Common Core alignment.
See which resources are available on this site for each element of the Common Core standards.
Check it out
