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Question -

Afarmer was having a field in the form of a parallelogram PQRS. She took anypoint A on RS and joined it to points P and Q. In how many parts the field isdivided? What are the shapes of these parts? The farmer wants to sow wheat andpulses in equal portions of the field separately. How should she do it?



Answer -

From the figure, it can beobserved that point A divides the field into three parts. These parts aretriangular in shape тИТ ╬ФPSA, ╬ФPAQ, and ╬ФQRA

Areaof ╬ФPSA + Area of ╬ФPAQ + Area of ╬ФQRA = Area of┬аPQRS тАж (1)

We know that if aparallelogram and a triangle are on the same base and between the sameparallels, then the area of the triangle is half the area of the parallelogram.

тИ┤ Area (╬ФPAQ) =┬аArea (PQRS) тАж (2)

From equations (1) and(2), we obtain

Area(╬ФPSA) + Area (╬ФQRA) =┬аArea (PQRS) тАж (3)

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

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