# 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?

$Fromthefigure,itcanbeobservedthatpointAdividesthefieldintothreeparts.Thesepartsaretriangularinshape-\Delta PSA,\Delta PAQ,and\Delta QRA\phantom{\rule{0ex}{0ex}}Areaof\Delta PSA+Areaof\Delta PAQ+Areaof\Delta QRA=Areaof\parallel gmPQRS...\left(1\right)\phantom{\rule{0ex}{0ex}}Weknowthatifaparalle\mathrm{log}ramandatriangleareonthesamebaseandbetweenthesameparallels,thentheareaofthetriangleishalftheareaoftheparalle\mathrm{log}ram.\phantom{\rule{0ex}{0ex}}\therefore Area\left(\Delta PAQ\right)=\frac{1}{2}Area\left(PQRS\right)...\left(2\right)\phantom{\rule{0ex}{0ex}}Fromequations\left(1\right)and\left(2\right),weobtain\phantom{\rule{0ex}{0ex}}Area\left(\Delta PSA\right)+Area\left(\Delta QRA\right)=\frac{1}{2}Area\left(PQRS\right)...\left(3\right)\phantom{\rule{0ex}{0ex}}Clearly,itcanbeobservedthatthefarmermustsowwheatintriangularpartPAQandpulsesinothertwotriangularpartsPSAandQRAorwheatintriangularpartsPSAandQRAandpulsesintriangularpartsPAQ.$

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