Question

"Question 6 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 field 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?

Class 9 - Math - Areas of Parallelograms and Triangles Page 160"

Answer 1

If a parallelogram and a triangle are on the same base and between the same parallels then area of the triangle is half the area of the parallelogram.

===========================================================

Given: PQRS is a parallelogram and A is any point RS.

Now join AP and AQ. Thus, the field will be divided in 3 parts and each part is in the shape of triangle.

Since , ∆APQ & parallelogram PQRS lie on the same base PQ and between same Parallel Lines PQ & SR.

 

ar(∆APQ)= ½ ar(||gm PQRS)........(i)

 

Then, remaining

ar(∆ASP)+ ar(∆ARQ)= ½ ar(||gm PQRS)........(ii)

From eq (i) & (ii)

ar(∆APQ)= ar(∆ASP)+ar(∆ARQ)

 

So farmer has two options:

 either the farmer can sow wheat in ∆APQ and pulses in other two Triangles or pulses in ∆APQ  and wheat in other two triangles.

 =========================================================

Hope this will help you...

 

Answer 2

Answer:

the field are divided into 3 part .