Quadrilaterals

Types of  quadrilateral

Mainly quadrilaterals are of two types that is simple and complex

Convex and concave quadrilaterals are belongs to simple types and crossed

Quadrilaterals are of complex types.

what are the types of quadrilaterals and their properties

Convex quadrilateral

Concave quadrilateral

Intersecting quadrilateral

   we know a closed shape (two dimensional) surrounded by four simple lines is called quadrilateral. And now we will discuss all six types of quadrilaterals with properties and formulas in detail.

•    Rectangle
•    Square
•    Rhombus
•    Parallelogram
•    Trapezium
•    Kite

      and diagonals are bisect each other.

              

   some properties are listed below.

• Rectangle consists of four sides .out of four sides opposite sides are equal and parallel.
• all angles are right angle  .
• diagonals are in same length.
• diagonals bisect each other.
• A diagonal  divides the rectangle into two equal triangles.   
• likewise two diagonals creates four triangles after bisection in rectangle and opposite triangles formed by bisection are equal  .             

     formulas related to rectangles are listed below.

• area
• perimeter  

    First of all we should understand :what is area?

    area is nothing but the the enclosure part or surface surrounded by the four sides of rectangle.

     

     if ABCD is a rectangle AB,BC,CD and DA are four sides of it.

   then area of a rectangle is the enclosure part of ABCD rectangle.

    for this we have to multiply the two sides of a ABCD.

    AREA=AB*BC.

      OR we can write : l*w  (l stands for length and w stands for width).

      

    before remembering the formula for perimeter we should go through what does it mean

   perimeter. According to its meaning it is the continuous line forming the boundary of a closed           geometrical figure.

   if ABCD is a rectangle then its lines are  AB,BC,CD,DA.

   so its perimeter is the AB+BC+CD+AD

              we know AB=CD and BC =DA  .    (consider the above fig)

           perimeter:=2(AB + BC)

                            =2(l + w)

     Example:  find the perimeter of a rectangle whose length  and breadth are 11cm and 9cm respectively.

    Square is a quadrilateral with four equal sides and and four right angles.

what are the types of quadrilaterals and their properties

     1. Properties of square:-

         Properties of  a square are listed below.

                       

• All four sides are equal
• All angles are right angle
• Opposite sides are parallel to each other.
• The two diagonals are equal and bisect each other at 90°.
• The diagonal bisect vertex angle.

                   

• Area
• Perimeter                

 1. Area of a square is     = a²    where a is the length of  the sides of  a square.

 In a Euclidean geometry ,Rhombus is  a quadrilateral whose four sides are equal and opposite sides are parallel to each other.

 

   

      Valuable properties of Rhombus are listed below.

• A rhombus is  a quadrilateral, which means it has four sides and each of these sides are congruent.
• The opposite sides of a rhombus are parallel to each other.
• A rhombus has opposite angles that are congruent.
• The diagonals of a rhombus are perpendicular.
• The diagonals of a rhombus form four congruent interior triangles.
• The diagonals of a rhombus  bisect each other.
• A rhombus has all the properties of parallelogram. 

                                 1.Opposite sides are congruent.

                                 2.The opposite angles are congruent.

                                 3.The diagonals  bisect each other.

   

• All rhombuses are not square but all squares are rhombus.
• The diagonals of a rhombus bisect each other but do not have the same length.
• diagonals are angle bisector.

   1. Area.

   2.Perimeter.

  

      The formula for area=1/2*d₁*d₂.

    Answer:  According to formula area =1/2*d₁*d₂.

         area=1/2*d₁*d₂.

  Perimeter

                a²=25

  Parallelogram is a type of quadrilateral with two of its sides parallel. Opposite sides of a parallelogram are equal and opposite angles of parallelogram are of equal in measure. Or we can say a quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel.

•  Area
•  Perimeter

             =2(length + breadth)

        A trapezium is a type of quadrilateral in 2D shape which has only one set of parallel sides .Parallel sides are known as the bases and non parallel sides are legs of the Trapezium.

• One pair of opposite side is parallel
•  Consecutive angles are supplementary. i.e.  <A+<D=180°.
• The line that joins the mid point of two non parallel sides is always parallel to the base of the trapezium  (mid-segment=(AB+CD) /2).
• Sum of the internal angles is 360°.

Formulas of Trapezium

• Area
• Perimeter    

 Area

Kite

  Kite is special  quadrilateral with two pairs of equal adjacent sides.

 

• Kite has four sides
• Diagonals are perpendicular to each other.
• One of the Diagonal bisect other one.
• angles between unequal sides are equal.
• Kite is special  quadrilateral with two pairs of equal adjacent sides.    

Formulas of Kite

Area

      D2=short diagonal length.

 Perimeter

  Perimeter of the kite =2a+2b.

Formulas of quadrilaterals

  

1.What are the different types of quadrilaterals and their properties?   Ans –         Here is the list of type of quadrilaterals with their properties Rectangle – Rectangle consists of four sides .out of four sides opposite sides are equal and parallel. All angles are right angles. Square – All four sides are equal .All angles are right angle. Opposite sides are parallel to each other. The two diagonals are equal and bisect each other at 90°.The diagonal bisect vertex angle. Rhombus – The opposite sides of a rhombus are parallel to each other .A rhombus has opposite angles that are congruent. The diagonals of a rhombus are perpendicular. The diagonals of a rhombus form four congruent interior triangles. The diagonals of a rhombus bisect each other. Parallelogram– Opposite sides   are congruent and parallel of a parallelogram.   The opposite angles are congruent.  Consecutive angles are supplementary.  Diagonals bisect each other. Each diagonal of a parallelogram separates it into two congruent triangles.    Trapezium – One pair of opposite side is parallel. Consecutive angles are supplementary .Diagonals bisect each other. Kite – Kite has four sides .Diagonals are perpendicular to each other .One of the Diagonal bisect other one. Angles between unequal sides are equal. Kite is special quadrilateral with two pairs of equal adjacent sides.   2.What are the  formulas of quadrilateral? ANS-Formulas of quadrilaterals    Summary of quadrilateral formulas Types of Quadrilateral Area Rectangle Length*width Square Side*side Rhombus ½*diagonal1*diagonal2 Parallelogram Base*height Trapezium ½*sum of two parallel sides*height kite ½*diagonal1*diagonal2