Question

AREAS OF PARALLELOGRAMS AND TRIANGLES
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A farmer was having a field in the form of a parallelogram PQRS. She took any point A
on RS and joined it to points P and 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?(with figure)
it's urgent friends please answer soon ​

Answer 1

Step-by-step explanation:

The field is divided in three triangles. 

Since △APQ and parallelogram PQRS are on the same base PQ and between the same parallels PQ and RS. 

∴ar(APQ)=21ar(PQRS)

⇒2ar(APQ)=ar(PQRS) 

But,

ar(PQRS)=ar(APQ)+ar(PSA)+ar(ARQ)(From fig.)

⇒2ar(APQ)=ar(APQ)+ar(PSA)+ar(ARQ)

⇒ar(APQ)=ar(PSA)+ar(ARQ)

Thus, area of △APQ=area of △PSA+area of △ARQ

To sow wheat and pulses in equal portions of the field separately, farmer should sow wheat in △APQ and pulses in other two triangles or pulses in △APQ and wheat in other two triangles.