Let quadrilateral ABCD bethe original shape of the field.
The proposal may beimplemented as follows.
Join diagonal BD and drawa line parallel to BD through point A. Let it meet
the extended side CD ofABCD at point E. Join BE and AD. Let them intersect each other at O. Then,portion ╬ФAOB can be cut from the original field so that the new shape of thefield will be ╬ФBCE. (See figure)
We have to prove that thearea of ╬ФAOB (portion that was cut so as to construct Health Centre) is equalto the area of ╬ФDEO (portion added to the field so as to make the area of thenew field so formed equal to the area of the original field)
It can be observed that╬ФDEB and ╬ФDAB lie on the same base BD and are between the same parallels BD andAE.
тИ┤Area (╬ФDEB) = Area (╬ФDAB)
тЗТArea (╬ФDEB) тИТ Area (╬ФDOB) = Area (╬ФDAB) тИТ Area (╬ФDOB)
тЗТ Area (╬ФDEO) = Area (╬ФAOB)