Answer :

Let quadrilateral ABCD be the original shape of the field

The proposal may be implemented as follows:


Join diagonal BD and draw a line parallel to BD through point A.

Let it meet the extended side CD of ABCD at point E.

Join BE and AD. Let them intersect each other at O.

Then, portion ΔAOB can be cut from the original field so that the new shape of the field will be ΔBCE



We have to prove that the area of ΔAOB (portion that was cut so as to construct Health Centre)

is equal to the area of ΔDEO (portion added to the field so as to make the area of the new field so formed equal to the area of the original field)




It can be observed that ΔDEB and ΔDAB lie on the same base BD and are between the same parallels BD and AE

So,

Area (ΔDEB) = Area (ΔDAB)


Area (ΔDEB) − Area (ΔDOB) = Area (ΔDAB) − Area (ΔDOB)


Area (ΔDEO) = Area (ΔAOB)

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