The diagonals of a parallelogram ABCD intersect at O. A line through O meets AB at X and CD at Y. Show that ar (parallelogram AXYD) = 1/2 ar (parallelogram ABCD)

Since, a diagonal of a parallelogram divides it into two triangles of equal area. Therefore, diagonal AC of parallelogram ABCD divides it into two triangles of equal area.