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What is a Square? / video tutorials
What is a square? Geometric Shapes
Square
s
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
s
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
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.