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The Properties of a Square
 Definitions and formulas for the perimeter of a square, the area of a square,  how to find the length of the diagonal of a square, properties of the diagonals of a square
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perimeter of a square area of a square sides and angles
of a square
diagonal of a square central angle of a square facts about squares

The perimeter of a square:

To find the perimeter of a square, just add up all the lengths of the sides:

Perimeter = x+x+x+x = 4x

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The area of a square:
To find the area of a square, multiply the lengths of two sides together...  Another way to say this is to say "square the length of a side!"  Get it?  Square!

Area = x*x = x^2
The sides and angles of a square:

square

The sides of a square are all congruent (the same length.)

The angles of a square are all congruent (the same size and measure.)

Remember that a 90 degree angle is  called a "right angle."  So, a square has four right angles.

Opposite angles of a square are congruent.
Opposite sides of a square are congruent.
Opposite sides of a square are parallel.
The diagonal of a square:

square

 To find the length of the diagonal of a square,  multiply the length of one side by the square root of 2:

If the length of one side is x...

length of diagonal = xsquare root of 2

 

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The central angle of a square:

square

 The diagonals of a square intersect (cross) in a 90 degree angle.  This means that the diagonals of a square are perpendicular.

The diagonals of a square are the same length (congruent).

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Cool facts about squares:
A square is a rectangle. A square is a trapezoid.
A square is a parallelogram. A square is a rhombus.
So, what's left?  A kite!  Is a square a kite?  I've seen "yes" and "no."  It all depends on whether or not you think a kite can have all its sides be the same length or not (which would make it a rhombus.)  I've seen some definitions where a kite must have two sides of length A and two sides of length B where A does not equal B.

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