**Common Core Standard 7.G.6**

### What is a Square? / video tutorials

# What is a square? Geometric Shapes

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*

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 angles congruent

- Two pairs of parallel sides

** A square has all the properties of rectangle.**

- Four right angles at the vertices

- 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.**

- 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

**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

### Square

**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

**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

- 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.