Like us!

Have a Look!

WhatsApp Message

Share Link

Relation between Area of Parallelogram and Triangle

Areas Of Parallelograms And Triangles II - Concepts

Median and Altitude of Triangle

Triangles on Same Base and Between Same Parallels

Relation between Area of Parallelogram and Triangle

Class - 9th CBSE Subjects

Concept Explanation

Relation between Area of Parallelogram and Triangle

Theorem: If a triangle and a parallelogram are on the same base and between the same parallels the area of the triangle is equal to half of the parallelogram.

Given A $Delta ABC$ and a $parallel ^{gm} BCDE$ on the same base BC and between the same parallels BC and AD

To prove $ar(Delta ABC)=frac{1}{2}ar(parallel ^{gm}BCDE)$

Construction Draw $AL perp BC;;and;;DM perp BC$ , meeting $BC$ in $M$

Proof Since A, E and D are collinear and BC || AD

$therefore$ $AL=DM$ ...(i) [ $because$ Distance between parallel lines is always same]

Now, $ar(Delta ABC)=frac{1}{2}(BCtimes AL)$

$Rightarrow ar(Delta ABC)=frac{1}{2}(BCtimes DM)$ ............(1) $[because AL=DM (from(i))]$

$large ar(parallel ^{gm}BCDE)= BC ;times;DM$ ...............(2)

From Eq (1) and Eq (2)

$Rightarrow ar(Delta ABC)=frac{1}{2}ar(parallel ^{gm}BCDE)$

ILLUSTRATION P and Q are any two points lying on the side DC and AD respectively of a parallelogram ABCD. Show that ar(APB)= ar(BQC)

Solution: Now $large parallel ^{gm}$ ABCD and $large Delta$ ABP lie on the same base AB and between the same parallel AB || CD

$Rightarrow ar(Delta ABP)=frac{1}{2}ar(parallel ^{gm}ABCD)$ .................. (1)

Similarly $large parallel ^{gm}$ ABCD and $large Delta$ BCQ lie on the same base BC and between the same parallel BC || AD

$Rightarrow ar(Delta BCQ)=frac{1}{2}ar(parallel ^{gm}ABCD)$ .................. (2)

From Eq (1) and Eq (2)

$ar(Delta ABP)=ar(Delta BCQ)$

Hence Proved

Sample Questions

(More Questions for each concept available in Login)

Question : 1

X and Y are respectively two points on the sides DC and AD of the parallelogram $ABCD$ . The area of triangle $BYC$ is equal to :
A. $frac{1}{2}times area;;of ;;triangle;;ABX$	B. $2times area;;of ;;triangle;;ABX$	C. $frac{1}{3}times area;;of ;;triangle;;ABX$	D. $area;;of ;;triangle;;ABX$
Right Option : D
View Explanation

Question : 2

If KLMN is a parallelogram and a KOL is a triangle with area x $m^2$ , then the area (KLMN) is _________________
A. 2x $m^2$	B. x $m^2$	C. 3x $cm^2$	D. 2x $cm^2$
Right Option : A
View Explanation

Question : 3

X and Y are respectively two points on the sides DC and AD of the parallelogram $ABCD$ . The area of triangle $ABX$ is equal to _______________.
A. $frac{1}{3}times area;;of ;;triangle;;BYC$	B. $area;;of ;;triangle;;BYC$	C. $frac{1}{2}times area;;of ;;triangle;;BYC$	D. $2times area;;of ;;triangle;;BYC$
Right Option : B
View Explanation

Video Link - Have a look !!!

Language - English

Chapters

Polynomials II

Linear Equations in One Variable

Introduction to Euclids Geometry

Herons Formula Complete

Polynomial I

Surface Area and Volume II

Surface Area and Volume I

Coordinate Geometry

Areas Of Parallelograms And Triangles II

Areas Of Parallelograms And Triangles I

Linear Equations in Two Variables

Content / Category

IMO-Mathematics Olympiad

Central Government Service

ISO - Science Olympiads

State Government Services

Banking And Insurance

Railways & Metro Services

MBA Entrance

Law Entrance

English Proficiency

Reasoning Proficiency

Computer Proficiency

Navodaya Entrance 6th & 9th

Sainik School Entrance

Class / Course

Students / Parents Reviews [10]

One of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develo...

Aman Kumar Shrivastava

10th

My experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.

Ayan Ghosh

8th

I have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying

Yatharthi Sharma

10th

It has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice

Barkha Arora

10th

It was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.

Eshan Arora

8th

Being a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from m...

Prisha Gupta

8th

Abhyas is a complete education Institute. Here extreme care is taken by teacher with the help of regular exam. Extra classes also conducted by the institute, if the student is weak.

Om Umang

10th

Abhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.

Manish Kumar

10th

My experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.

Hiya Gupta

8th

It was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.

Cheshta

10th

View All

Attention !!!!!

Relation between Area of Parallelogram and Triangle

Relation between Area of Parallelogram and Triangle

Students / Parents Reviews [10]

Aman Kumar Shrivastava

Ayan Ghosh

Yatharthi Sharma

Barkha Arora

Eshan Arora

Prisha Gupta

Om Umang

Manish Kumar

Hiya Gupta

Cheshta