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diagonal of a square formula
Common Core Standard  7.G.6

What is a Square? / video tutorials

What is a square? Geometric Shapes

A Square
In this video you will learn ..

How to calculate the perimeter of a square

How to find the perimeter given the diagonal of a square

Equation for finding the perimeter of a square

Perimeter of Square Practice Problems
In this video you will learn ..

How to calculate the area of a square

The formula for area of a square

How to calculate the area given the diagonal of a square

​ A square has all the properties of a parallelogram. 
  • Opposite sides congruent
  • Opposite angles congruent
  • Two pairs of parallel sides

 A square has all the properties of rectangle.
  • Four right angles at the vertices
  • Diagonals are congruent
  • Diagonals bisect each other
  • Diagonals form two pairs of congruent, isosceles triangles
All of the sides of a square are congruent length therefore,
  • The angle measure of all of the sides are right angles. 
  • The opposite angles of a square are congruent
  • The opposite sides of a square are congruent
  • The opposite sides of a square are parallel

Tip: Congruent means the same shape or size. In other words " equal"

 A square has all the properties of rhombus.
  • Four congruent sides
  • Diagonals cross at right angles in the center
  • Diagonals form 4 congruent right triangles
  • Diagonals bisect each other 
  • Diagonals bisect the angles at the vertices

Properties and Attributes of a Square

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Formulas for diagonal length, area, and perimeter of a square
  • The Area of a square is equal to side * side or S^2
  • The perimeter of a square equals s+s+s+s or 4(s)
  • The formula for the length of the diagonal of a square equals: s√2

Formulas of a Square

= Right Angle
= Congruent


Diagonal Formulas of a Square

-Diagonal Formula of a square using a side = d = x·√2

-Diagonal of a Square using area - d = √2A 
where A = area of the square

-Diagonal length using perimeter - d =P2√2 
where P = perimeter of the square

Area formulas of a Square

-Area of a square using sides - A = x^2

-Area of a square using perimeter-A = P^2/16
where P = perimeter

-Area of a square using the diagonal- A = d^2/2
where d = diagonal length

area of a square
Perimeter formulas of a Square

Perimeter of a square using the sides- 4x

Perimeter using diagonal length-  2d√2

Perimeter using area of a square- 4√A
where A = Area of the Square

perimeter of a square
  • Is a square a rhombus? yes
  • Is a square a parallelogram? yes
  • Is a square a rectangle? yes

Many people in Geometry will call the square the perfect quadrilateral. Why?
Because all the characteristics of a paralleogram, rectangle, and rhombus.

Let's explore the properties of a square.