Q22 of 31 Page 232

PQRS is a parallelogram X and Y are the mid points of side PQ and SR respectively. Join diagonal SQ. Let us write area of the parallelogram shaped region XQRY : area of triangular region QSR.


In parallelogram PQRS and XQRY


Area of PQRS = SR × Height


Area of XQRY = YR × Height


YR = × SR


Area of parallelogram XQRY = × SR × Height


=× Area of parallelogram PQRS


In parallelogram PQRS and triangle QSR


Both lies on same base SR


And both are between parallel lines


∴ Area of triangle QSR = × Area of parallelogram PQRS


Area of triangle QSR = Area of parallelogram XQRY


Area of triangle QSR : Area of parallelogram XQRY


1 : 1


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