Properties of Squares

Squares are the most exclusive of all the quadrilaterals we have learned, because they have the most restrictions upon them. Since squares are parallelograms, they have two pairs of parallel sides and diagonals bisect each other. They are also rectangles, so they also have four right angles. But wait, there's more! They are also rhombuses, so all of their sides are equal and their diagonals are perpendicular! Amazing right?!

Area and Perimeter of Squares

Just when you thought squares couldn't get any cooler, you realize how easy it is to find their perimeter and area. To find the area of a square, all you have to do is square the length of one side! To find perimeter, just multiply the length of one side by four! Defining the side length as S, gives you the following equations:

$A = S^2$ and $P = 4S$

Some other interesting properties

The diagonal of a square will always be $\sqrt{2}S$. This can easily be proven. If you look closely, you can see that triangle ACD is a 45-45-90 right triangle. For more information on those, read "Special Right Triangles" here. Using the properties of 45-45-90 triangles, it is easy to see why this is true.

Squares have four lines of symmetry, two diagonal, one horizontal, and one vertical.

All in all, squares are some pretty awesome quadrilaterals.

Squares are the most exclusive of all the quadrilaterals we have learned, because they have the most restrictions upon them. Since squares are parallelograms, they have two pairs of parallel sides. They are also rectangles, so they also have four right angles. But wait, there's more! They are also rhombuses, so all of their sides are equal! Amazing right?!

Area and Perimeter of Squares

Just when you thought squares couldn't get any cooler, you realize how easy it is to find their perimeter and area. To find the area of a square, all you have to do is square the length of one side! To find perimeter, just multiply the length of one side by four! This gives you the following equations:

$A = S^2$ and $P = 4S$

Some other interesting properties

To be completed at a later time.

All four sides are equal in length

All angles are right angles.

The diagonals of a square bisect each other perpendicularly.

The diagonals of a square bisects its angles.

The diagonals are equal in length.

A square is a unique case of rhombus as well as rectangle.

Each diagonal divides the square into two 45-45-90 right triangles.