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December 11, 2024Properties 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.
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 \(PSQR,\,SRPQ,\,RSQP,\,SPRQ\).
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.
Below we have highlighted the different types of quadrilaterals and the properties of each figure that differentiates one from another:
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 kite if it has two pairs of equal adjacent sides but4 unequal opposite sides.
The properties of the kite are as written below:
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The type of quadrilateral having all sides equal is called a rhombus.
The properties of the rhombus are as written below:
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:
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:
The type of quadrilateral having exactly one pair of parallel sides is called the trapezium.
The properties of the trapezoid are as written below:
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 |
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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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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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.
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:
Q.2: What are the seven quadrilaterals?
Ans: The seven quadrilaterals are given below:
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:
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.
Q.5: What are the six special quadrilaterals?
Ans: The quadrilaterals are divided into the following six (\(6\)) types:
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.
We hope this detailed article on the properties of quadrilaterals helps you. If you have any queries regarding this article, reach out to us through the comment section below and we will get back to you as soon as possible. Stay tuned to Embibe for the latest news and updates on quadrilateral properties.