Cool math .com - The Properties of a Square (perimeter, area, interior angles, diagonals, lengths of sides)

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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

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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

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 = x

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).

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.