Properties of Quadrilaterals: A quadrilateral is a four-sided polygon bordered by four finite line segments. The term ‘quadrilateral’ is derived from the Latin words ‘quadra’ (four) and ‘Latus’ (sides). A quadrilateral’s four sides may or may not be equal. It is important to learn the properties of Quadrilaterals to understand the concepts thoroughly. 

Although a quadrilateral has four sides, four angles, and four vertices, the lengths of the sides and angles vary. It should be noted that the sum of a quadrilateral’s internal angles is always equal to 360°. On this page, we’ll discuss everything about the properties of quadrilaterals, their definition, and solved problems. Read further to find more.

Properties of Quadrilaterals Chart

The quadrilateral is a closed two-dimensional shape formed by joining four points, among which three points are not collinear. A quadrilateral has four sides, four angles, and four vertices or corners. Let us understand the properties of any quadrilateral with the help of an example:

Let \(PQRS\) be a quadrilateral. We should name the quadrilateral in order as
\(PQRS,\,QRSP,\,RSPQ,\,SPQR\) but not \(PSQR,\,SRPQ,\,RSQP,\,SPRQ\).

• \(PQ,\,QR,\,RS\) and \(SP\) are the \(4\) sides.
• Point \(P,\,Q,\,R\) and \(S\) are \(4\) vertices or corners.
• \(∠PQR,\,∠QRS,\,∠RSP\) and \(∠SPQ\) are \(4\) angles.
• \(PS\) and \(QR\) are opposite sides.
• \(PQ\) and \(QR\) are adjacent sides.
• \(∠Q\) and \(∠S\) are opposite angles.
• \(∠Q\) and \(∠R\) are adjacent angles.
• The total of four interior angles of any quadrilateral is \(360^\circ\).

Special quadrilaterals consist of the four-sided figures square, rectangle, parallelogram, rhombus,  trapezium and kite. So, the properties of a quadrilateral will be a collection of the properties of all these figures. Students can also download properties of quadrilaterals pdf to keep it as a reference for later.

Examples of Quadrilaterals:

Below we have highlighted the different types of quadrilaterals and the properties of each figure that differentiates one from another:

Properties of Parallelogram

A quadrilateral is called a parallelogram if both pairs of its opposite sides are parallel.
The properties of the parallelogram are as written below:

• A quadrilateral is called a parallelogram if both pairs of its opposite sides are parallel and are of equal length.
• The diagonals of the parallelogram bisect each other.
• The opposite angles are of equal measure.
• The pair of adjacent angles are supplementary.

Properties of Kite

A quadrilateral is called a kite if it has two pairs of equal adjacent sides but4 unequal opposite sides.
The properties of the kite are as written below:

• A quadrilateral is called a kite if it has \(2\) pairs of equal adjacent sides but unequal opposite sides.
• The larger diagonal of the kite bisects the smaller diagonal.
• Only one pair of opposite angles are of the same measure.

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Properties of Rhombus

The type of quadrilateral having all sides equal is called a rhombus.
The properties of the rhombus are as written below:

• It is a type of parallelogram having all sides equal.
• The opposite sides are parallel to each other.
• The opposite angles are of the same measure.
• The total of any two adjacent angles is equal to \(180^\circ\).
• The diagonals of a square bisect each other perpendicularly.

Properties of Rectangle

The type of quadrilateral in which opposite sides are of equal length, but adjacent sides are not equal, and each angle is a right angle is called a rectangle.
The properties of the rectangle are as written below:

• It is a type of quadrilateral in which the opposite sides are of equal length.
• Adjacent sides are not equal in length
• Each interior angle is a right angle or \(90^\circ\).
• Opposite sides are parallel to each other.
• The diagonals of a rectangle bisect each other, but not perpendicularly.

Properties of Square

The type of quadrilateral in which all the sides are equal, and each angle measures \(90^\circ\) is called a square.
The properties of the square are as written below:

• All the sides of a square are equal.
• Each angle measures \(90^\circ\) i.e. right angle.
• The sides are parallel to each other.
• The diagonals of a square bisect each other perpendicularly.

Properties of Trapezoid

The type of quadrilateral having exactly one pair of parallel sides is called the trapezium.
The properties of the trapezoid are as written below:

• The type of quadrilateral having exactly one pair of parallel sides is called the trapezium.
• It has two parallel sides and two non-parallel sides.
• The parallel sides are called “bases” and the non-parallel sides are called “legs” or lateral sides.
• Two adjacent angles are supplementary.
• Trapezoid are of two types: scalene trapezium and isosceles trapezium
• In scalene trapezium, the non-parallel sides are different in length
• In isosceles trapezium, the non-parallel sides are the same in length
• In isosceles trapezium, the diagonals bisect each other.

What Are the Quadrilateral Formulas?

Perimeter formulae of quadrilaterals:

Name of Quadrilateral	Perimeter Formula
Rhombus	\(4 \times \rm{Side}\)
Square	\(4 \times \rm{Side}\)
Rectangle	\(2 \times \left( {{\rm{Length}} + {\rm{Breadth}}} \right)\)
Parallelogram	\(2 \times \left( {{\rm{Sum}}\,{\rm{of}}\,{\rm{the}}\,{\rm{adjacent}}\,{\rm{sides}}} \right)\)
Kite	\(2 \times (a + b) \) where \(a\) and \(b\) are the lengths of the unequal sides

Area Formulae of Quadrilaterals

The area of any shape is the space covered by it. The formula of area of some quadrilaterals are given below:

Name of Quadrilateral	Area Formula
Square	\(\rm{Side} \times \rm{Side}\)
Rectangle	\(\rm{Length} \times \rm{Breadth}\)
Parallelogram	\(\rm{Base} \times \rm{Height}\)
Rhombus	\(\frac{1}{2} \times {\text{Product}}\,{\text{of}}\,{\text{the}}\,{\text{diagonals}}\)
Kite	\(\frac{1}{2} \times {\text{Product}}\,{\text{of}}\,{\text{the}}\,{\text{diagonals}}\)

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Solved Examples: Properties of Quadrilaterals Diagonals

Q.1. How many sides and vertices, a quadrilateral has?
Ans: A quadrilateral has 4 sides and 4 vertices.

Q.2. How many angles and diagonals, a quadrilateral has?
Ans: A quadrilateral has 4 angles and 2 diagonals.

Q.3. What is the area of a rectangle, if its length is \(9\;\rm{m}\) and breadth is \(5\;\rm{m}\).
Ans: Given,
The length of the rectangle = 9 m
The breadth of the rectangle = 5 m
We know that the area of a rectangle =Length×Breadth
Now, the area of the rectangle =9m×5m=45m²
Hence, the area of the rectangle is = 45m²

Q.4. Find the perimeter of the below figure.

Ans: Given, the length of the sides of the figure is 3cm, 3cm, 5cm and 4cm
We know that perimeter of the figure \(=\) sum of the length of all the sides
Now, perimeter of ABCD=3cm+3cm+5cm+4cm=15cm.
Hence, the perimeter of the given figure is 15 cm.

Q.5. If the side of a square is \(6\;\rm{m}\), find its area.
Ans: Given, the length of the side of a square = 5m
We know that the area of a square = Side * Side
Now, the area = 6m×6m=36m²
Hence, the area of the square is 36m².

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Summary of Properties of Quadrilaterals PDF

In this article, we have covered the term quadrilaterals. We talked about the quadrilateral properties that included properties of a square, properties of a rhombus, properties of a rectangle, properties of a parallelogram, properties of the kite, properties of the trapezoid. Then we glanced at the formulas of the perimeter and the area of the quadrilaterals. Then we discussed the solved examples along with a few FAQs.

FAQs on Features of Quadrilateral

Q.1: What are the 4 properties of a quadrilateral?
Ans: A quadrilateral is a two-dimensional closed figure having four arms or edges or sides.
The 4 properties of a quadrilateral are:

• It has 4 sides.
• It has 4 angles.
• It has 4 vertices or corners.
• The total of four interior angles is 360 degrees.

Q.2: What are the seven quadrilaterals?
Ans: The seven quadrilaterals are given below:

• Kite
• Parallelogram
• Trapezoid (US) and Trapezium (UK)
• Isosceles Trapezoid
• Rectangle
• Square and
• Rhombus.

Q.3: What are the properties of the quadrilateral kite?
Ans: A quadrilateral is called a kite with two pairs of equal adjacent sides but unequal opposite sides. To be classified as a kite, a figure should have the following properties:

• A quadrilateral is called a kite with two pairs of equal adjacent sides but unequal opposite sides.
• The larger diagonal of the kite bisects the smaller diagonal in right angles.
• Only one pair of opposite angles are of the same measure.

Q.4: What are the properties of the quadrilateral rectangle?
Ans: The type of quadrilateral in which opposite sides are of equal length, and each angle is a right angle is called a rectangle.

• It is a type of quadrilateral in which the opposite sides are of equal length.
• Each angle is a right angle or \(90^\circ\).
• Opposite sides are parallel to each other.
• The diagonals of a rectangle bisect each other, but not perpendicularly.

Q.5: What are the six special quadrilaterals?
Ans: The quadrilaterals are divided into the following six (\(6\)) types:

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

Q.6: How do you classify quadrilaterals?
Ans: Quadrilaterals are classified, and they are identified based on the lengths and angles of the side. While each four-sided shape is quadrilateral, sometimes there is a more specific name. The parallelogram is a quadrilateral with opposite sides, and they are parallel and congruent. Congruent means the same.

Q.7: How do you identify a quadrilateral?
Ans: A quadrilateral is identified by a two-dimensional closed figure having 4 sides, 4 corners, 4 angles, and the sum of four interior angles is 360 degrees.

Q.8: What does quadrilateral mean?
Ans: The word “quadrilateral” is derived from the two Latin words “quadri” which means four and “latus” which means sides. So, a quadrilateral is a plane closed figure having four sides.

Now you are provided with all the necessary information regarding the properties of quadrilaterals. Practice more questions and master this concept. You can make use of NCERT Solutions for Maths provided by Embibe for your exam preparation.

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