Question

6. A farmer was having a field in the form of a parallelogram PQRS. She took any point
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 1

Field is Divided into three Parts , Area of middle is Equal to Sum of Area of two corner

Step-by-step explanation:

Let say point on RS is   A

Field is divided into three Triangular Parts

ΔPAS  , ΔPAQ  &  ΔQAR

Area of ΔPAQ = (1/2)PQ  * Altitude     ( ⊥ distance  between PQ & RS)

Area of ΔPAS = (1/2)AS  * Altitude     ( ⊥ distance  betwenn PQ & RS)

Area of ΔQAR = (1/2)AR  * Altitude     ( ⊥ distance  betwenn PQ & RS)

Area of ΔPAS  + Area of ΔQAR  = (1/2) (AS + AR) * Altitude

=  (1/2) (RS) * Altitude

= (1/2) (PQ) * Altitude    ( PQ = RS  opposite side of parallelogram)

= Area of ΔPAQ

Area of ΔPAQ = Area of ΔPAS + Area of ΔQAR

if farmer wants to sow wheat and pulses in equal portions of the field separately

then He should plant one of them in field PAQ

and another in field PAS & QAR

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