Square-
A Quadrilateral with four right angles and four congruent sides
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square properties

4 right angles
the width is smaller then the length
opposites are congruent lengths is a fourth of the width
4 equal sides 4 congruent sides
diagonal bisect each other
diagonals the same
the parallelogram and the rhombus have same properites of the square

The perimeter of a square whose sides have length t is
p=4t
and the area is
a=4exponet2

In classical times, the second power was described in terms of the area of a square, as in the above formula. This led to the use of the term square to mean raising to the second power.

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 = 4swhere 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 = s2where 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
s is the length of any one side

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