Question

"Question 12 A villager Itwaari has a plot of land of the shape of a quadrilateral. The Gram Panchayat of the village decided to take over some portion of his plot from one of the corners to construct a Health Centre. Itwaari agrees to the above proposal with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented.

Class 9 - Math - Areas of Parallelograms and Triangles Page 164"

Answer 1

Two Triangles on the same base and between the same parallels are equal in area.

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Let ABCD be the plot of the land of the shape of a quadrilateral.

Construction,

Diagonal BD is joined. AE is drawn parallel BD. BE is joined which intersected AD at O. △BCE is the shape of the original field and △AOB is the area for constructing health centre. Also, △DEO land joined to the plot.

To prove:
ar(△DEO) = ar(△AOB)

Proof:

△DEB and △DAB lie on the same base BD and between the same parallel lines BD and AE.

ar(△DEB) = ar(△DAB)

 ar(△DEB) – ar△DOB) = ar(△DAB) – ar(△DOB)

[ On subtracting ar(△DOB) from both sides]

 ar(△DEO) = ar(△AOB)

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Hope this will help you...

 

Answer 2

Hi friend ✨✨✨

Let -ABCD be the quadrilateral plot.Produce BA to meet DE drawn parallel to CA at E .Join EC.

Then , triangle EAC and ADC lie on the same parallel DE and CA

ar (EAC)=ar(ADC)

NOW, ar(-ABCD)= ar(ABC)+ar(ACD)

ar(ABC)+ar(ADC)


ar(ABC)+ar( EAC). =ar(EBC)

quad.ABCD = ∆EBC


Which is the required explain to the suggestion proposal.

thanks.....