what are the types of quadrilaterals and their properties
Quadrilaterals
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 .
Quadrilateral ABCD
The sum of the interior angles of a simple (and planar) quadrilateral ABCD is 360 °, i.e.
<A+ <B+<C+<D=360°.
Types of quadrilateral
Convex quadrilateral
Concave quadrilateral
Intersecting quadrilateral/crossed 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
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.
Concave quadrilateral
At least one of the diagonals lies partly or entirely outside of the figure.
Intersecting quadrilateral
Intersecting quadrilaterals are not simple quadrilaterals in which pair of non-adjacent sides intersect .This kind of quadrilaterals are known as self-intersecting or crossed quadrilaterals.
Shapes of quadrilaterals
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
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)
=2(length + breadth)
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
Kite is special quadrilateral with two pairs of equal adjacent sides.
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.
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
Types and Hierarchy of Quadrilaterals
what are the types of quadrilaterals and their properties
Frequently Asked Questions
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 quadrilateralwith two pairs of equal adjacent sides.