# what are the types of quadrilaterals and their 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 quadrilaterals are of two types that is simple and complexConvex and concave quadrilaterals are belongs to simple types and crossedQuadrilaterals are of complex types. what are the types of quadrilaterals and their properties Convex quadrilateral

In a convex quadrilateral, all interior angles are less than 180 ° and both  the diagonals of a quadrilateral are completely contained within a figure.
• Rectangle
• Square
• Rhombus
• Parallelogram
• Trapezium
• Kite.

At least one of the diagonals lies partly or entirely outside of the figure.

 what are the types of quadrilaterals and their properties

## Different types of quadrilaterals with Properties and formulas

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

### Rectangle

A quadrilateral with four right angles and out of four sides, opposite sides are equal and parallel
and diagonals are bisect each other.

### 1.Properties of Rectangle:-

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  .

### 2. Formulas of Rectangle:

formulas related to rectangles are listed below.
• area
• perimeter

### Area:

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).

Example: Find the area of a rectangle whose sides are 5cm and 4 cm respectively.

w=4cm
then area : =l*w
=5*4
=20 cm²

### Perimeter:

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.
so perimeter of the rectangle is  = 2(11+9)
=2(20)
=40cm

### Square

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.

### 2.Formulas of Square

• Area
• Perimeter
1. Area of a square is     = a²    where a is the length of  the sides of  a square.
2.   Perimeter of a square  = 4a   as all four sides of a square are equal.
3. ΔABC=ΔBCD=ΔCDA=ΔDAB= a² /2   (consider above square)
4.ΔAOB=ΔBOC=ΔCOD=ΔDOA= a²/4
5. Diagonal  AC=BD=a√2

As we know diagonals are bisect each other at 90° .So, we can apply Pythagoras

theorem h²=p²+b²

h²=a²+a²

h² =2a²

h=a√2

h is nothing but the AC=BD=h (diagonal).

Example:-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

### Rhombus

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

### Properties of Rhombus

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.

### Formulas of a Rhombus

1. Area.
2.Perimeter.

#### Area

The formula for area=1/2*d₁*d₂.

 what are the types of quadrilaterals and their properties

Example:-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.

#### Perimeter

The formula for perimeter =4a=4*side.
Example: Above question we can take to find the  perimeter. The diagonals are giving in above
example, we have to find the sides of rhombus first.
We know the diagonals of  rhombus are perpendicular to each other. Here we can apply Pythagoras
theorem to find sides.
h²=p²+b²     (consider the above figure)
a²=(d₁/2)²+(d₂/2)²  (As diagonals bisect each other)
a²=3²+4²
a²=9+16

a²=25

a=√25=5cm
Perimeter of the rhombus =4*5 =20cm.

### Parallelogram

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.
 what are the types of quadrilaterals and their properties

### Properties of Parallelogram

Some basic properties of a parallelogram are listed below.

•   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.

### Formulas of parallelogram

•  Area
•  Perimeter
Area

Area=  b*h
b=base of parallelogram
h=height of parallelogram

Perimeter

perimeter = 2(a + b)

### Trapezium

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.

 what are the types of quadrilaterals and their properties

### Properties of 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

Area=1/2*sum of two parallel sides*height or altitude .
Perimeter

Perimeter of the trapezium is =sum of all four sides.

### Kite

 what are the types of quadrilaterals and their properties

### 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.

### Formulas of Kite

• Area.
• Perimeter.

#### Area

Area of the Kite=1/2*D1D2

D1=long diagonal length.
D2=short diagonal length.
Perimeter
Perimeter of the kite =2a+2b.

 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

## Types and Hierarchy of Quadrilaterals

 what are the types of quadrilaterals and their properties

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.
• ParallelogramOpposite 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?