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Question

A farmer was having a field in the form of a parallelogram $ \mathrm{PQRS}$. She took any point $ \mathrm{A}$ on $ \mathrm{RS}$ and joined it to points $ \mathrm{P}$ and $ \mathrm{Q}$. In how many parts the fields is divided? What are the shapes of these parts? The farmer wants to sow wheat and pulses in equal portions of the field separately. How should she do it?

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Solution

As we observe from the figure, the field is divided into three parts each in triangular shape.

ΔPSA,ΔPAQandΔQAR are the triangles.

We know that,

Areaof(ΔPSA+ΔPAQ+ΔQAR)=AreaofPQRS(i)

AreaofΔPAQ=12areaofPQRS(ii)[Whenthetriangleandparallelogramareonthesamebaseandbetweenthesameparallellinesthen,Areaoftriangle=12Areaofparallelogram.

From (i) and (ii) we get,

AreaofΔPSA+AreaofΔQAR=12areaofPQRS(iii)

From (ii) and (iii), we can conclude that,

The farmer must sow wheat or pulses in ΔPAQ or either in both ΔPSAandΔQAR.


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