Question

A farmer has a field in the form of a parallelogram PQRS as shown in the figure. He took the mid- point A on RS and joined it to points P and Q. In how many parts of field is divided? What are the shapes of these parts?
The farmer wants to sow groundnuts which are equal to the sum of pulses and paddy. How should he sow? State reasons?

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.

solution :

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:

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