Squares

 

    A square is a quadrilateral in which all the sides are equal and all the angles are right angles. A square is a special type of rhombus, rectangle, and parallelogram:

    The formula for the area of a square is:

    where s is the length of a side of the square. Because all the sides of a square are equal, it is also possible to provide a simple formula for the perimeter: P = 4s, where s is, once again, the length of a side.

 

    A diagonal drawn into the square will always form two congruent 45-45-90 triangles:

    From the properties of a 45-45-90 triangle, we know that . In other words, if you know the length of one side of the square, you can easily calculate the length of the diagonal. Similarly, if you know the length of the diagonal, you can calculate the length of the sides of the square.