Maths / Areas Of Parallelograms And Triangles / Relation between Area of Parallelogram and Triangle

QUESTION
 

In the following figure, large AC parallel PSparallel QR;and;PQparallel DB parallel SR. Prove that area of quadrilateral large PQRS=2 times area of quadrilateral ABCD.

 

EXPLANATION
Explain TypeExplanation Content
Text

APSC is a parallelogram.

therefore : : : : : : : : : : : AC parallel PS

Now,  ar(Delta ADC)=frac {1}{2} ar(APSC) : : :  : : : : : : : : : ..........(1)

[Parallelogram and triangle on the same base and betweem the same parallel lines]

Similarly,

          ar(Delta ABC)=frac {1}{2} ar(ACRQ) : : : : : : : : : : : : ...............(2)

Adding (1) and (2), we get

ar(Delta ADC)+ar(Delta ABC)=frac {1}{2} (ar(APSC)+ar(ACRQ))

                 ar(ADCB)=frac {1}{2} ar(PQRS)

Rightarrow             ar(PQRS)=2ar(ABCD)

View Contents
(Concept based Learning and Testing for [6th - 10th], NTSE, Bank & Govt. Exams)
Self Learning
Testimonials
No Preview
Parent Feedback on Methodology c/o Aman Kumar Shrivastava C/o ABHYAS Academy
 10th
In terms of methodology I want to say that institute provides expert guidence and results oriented monitering supplements by requsite study material along with regular tests which help the students to improve their education skills.The techniques of providing education helps the students to assess their real preparation level.
Back
Courses We Offer
(Concept based Learning and Testing for [6th - 10th], NTSE, Bank & Govt. Exams)