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 into three parts.

The three parts are in the shape of triangle $△PSA,△PAQ$ and $△QAR$

Area of $△PSA+△PAQ+△QAR$ $=$ Area of $PQRS$ --- (i)

Area of $△PAQ=\frac{1}{2}$ area of $PQRS$ --- (ii)

Triangle and parallelogram on the same base and between the same parallel lines.

From (i) and (ii),

Area of $△PSA+$ Area of $△QAR=\frac{1}{2}$ area of $||gmPQRS$ --- (iii)

Clearly from (ii) and (iii),

Farmer must sow wheat or pulses in $△PAQ$ or either in both $△PSA$ and $△QAR$.