# Type of quadrilaterals and its properties| Diagrams

In this content ,we will come to know the types of quadrilateral   and the properties of quadrilaterals. Quadrilateral is consists of four sides. Here we define how many type of quadrilaterals are there and its properties .

The closed shape (two dimensional) surrounded by four simple lines is called quadrilateral. In Euclidean plane geometry, a quadrilateral is a type of polygon having four sides and four vertices .

The sum of the interior angles of a simple (and planar) quadrilateral ABCD is 360 °, i.e.
<A+ <B+<C+<D=360°.

Mainly There are Three types of Quadrilaterals.
In Other way  Types of  quadrilateral can be classified as
• Rectangle
• Square
• Rhombus
• Parallelogram
• Trapezium
• Kite.
 Type of quadrilaterals and its properties| Diagrams

# Types of  quadrilaterals and its properties with diagrams

• four sides
• four angles

sum of all four angles is 360°.

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

### Properties of Rectangle

 Type of quadrilaterals and its properties| Diagrams
• 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  .

### 2. Properties of square:-

Properties of  a square are listed below.
 Type of quadrilaterals and its properties| Diagrams

• 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.

### Properties of Rhombus

 Type of quadrilaterals and its properties| Diagrams
• 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.

### Properties of Parallelogram

 Type of quadrilaterals and its properties| Diagrams
•   Opposite sides   are congruent and parallel of a parallelogram.
•    The opposite angles are congruent.
•   Consecutive angles are supplementary . means<A+<D=180°.
•  Diagonals bisect each other.
•  Each diagonal  of a parallelogram separates it into two congruent triangles.

### Properties of  Trapezium

 Type of quadrilaterals and its properties| Diagrams
• One pair of opposite side of Trapezium 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°.

### Properties of 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.

#### Area

 Types of Quadrilateral Formulas 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

#### Perimeter

 Types of Quadrilateral Formulas of Quadrilateral:-Perimeter Rectangle 2(length + breadth) Square 4*side Rhombus 4*side Parallelogram 2(length + breadth) Trapezium sum of all four sides. kite sum of all four sides.
Some Examples on Types of Quadrilateral

1. Find the Area of  a Rectangle whose diagonal is 5 cm and one of its side is 3 cm.

Here diagonal and। One side is giving.

Applying Pythagoras rule we can find another side of the rectangle.

Another side=  √(5² -3²)=4cm.
So Area=3*4= 12cm² .

Example 2:-Find the area and perimeter of a square of side 8cm.

Answer:-Area of a square = a² .

so 8²=64 cm².

perimeter of a square= 4a

so perimeter of this square=4*8=32 cm.

Example 3:-Find the area of a rhombus whose diagonals are 6cm and 8cm respectively.

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

d₁=6cm
d₂=8cm
area=1/2*d₁*d₂.
= 1/2*6*8cm
=24cm².

#### Example 4:- Find quadrilaterals around us.

Answer; As we know  Quadrilateral  is a closed figure in two dimension having  four sides. And types of quadrilateral are rectangle, square, rhombus, parallelogram, trapezium and kite.
The things which are in shape of rectangle, square, trapezium, parallelogram, rhombus and  kite are said to be the  quadrilaterals around us.

• Mobile phone
• Tv
• Table
• kite
• Black board
• windows and doors
• Books
• Walls
• Photo frames
• Refrigerators
• Chess Board
• Playing Cards

etc. those are in  quadrilateral shapes (only shapes ).

1.How many types of quadrilateral are there?

Ans-Mainly six types of  quadrilateral are there.

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

• four sides
• four angles.
• sum of all four angles is 360°.                                                                                                                                                                                                                   According to the type of  quadrilaterals properties are listed in above content.

3. What is a quadrilateral formula?
Ans-  Types of Quadrilaterals with their formula

 Types of Quadrilaterals Area Perimeter Rectangle Length*width 2(length + breadth) Square Side*side 4*side Rhombus ½*diagonal1*diagonal2 4*side Parallelogram Base*height 2(length + breadth) Trapezium ½*sum of two parallel sides*height sum of all four sides. Kite ½*diagonal1*diagonal2 sum of all four sides.

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