Question

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?

Answer 1

The field is divided in three triangles. Since triangle APQ and parallelogram PQRS are on the same base PQ and between the same parallels PQ and RS. 

∴ ar (APQ) = 1/ 2 ar (PQRS) 

⇒ 2ar (APQ) = ar(PQRS) 

But ar (PQRS) = ar(APQ) + ar (PSA) + ar (ARQ) 

⇒ 2 ar (APQ) = ar(APQ) + ar(PSA) + ar (ARQ) 

⇒ ar (APQ) = ar(PSA) + ar(ARQ) 

Hence, area of ∆APQ = area of ∆PSA + area of ∆ARQ. 

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