Premium Online Home Tutors
3 Tutor System
Starting just at 265/hour

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 :

image

From the figure, we can say that it is that point A which divides the field into three parts.

These parts are triangular in shape i.e., \(\triangle{PSA}\), \(\triangle{PAQ}\) and \(\triangle{QRA}\)

Thus, Area \(\triangle{PSA}\) + Area \(\triangle{PAQ}\) + Area \(\triangle{QRA}\) = Area of Parallelogram PQRS ...(i)

Also, Area \(\triangle{PAQ}\) = (\(\frac{1}{2} \)) Area of Parallelogram PQRS ...(ii)

From equation (i) and (ii), we get,

Area \(\triangle{PSA}\) + Area \(\triangle{QRA}\) = \(\frac{1}{2}\) Area of Parallelogram PQRS ...(iii)

Clearly, it can be observed that the farmer must sow wheat in triangular part PAQ and pulses in other two triangular parts PSA and QRA or wheat in triangular parts PSA and QRA and pulses in triangular parts PAQ.

NCERT solutions of related questions for Areas of parallelograms and triangles

NCERT solutions of related chapters class 9 maths

NCERT solutions of related chapters class 9 science