Show that the diagonals of a parallelogram divide it into four triangles of equal area.

O is the mid point of AC and BD. (diagonals of a parallelogram bisect each other)
In ΔABC, BO is the median. ∴ar(AOB)=ar(BOC) — (i)
Also, In ΔBCD, CO is the median. ∴ar(BOC)=ar(COD) — (ii)
In ΔACD, OD is the median. ∴ar(AOD)=ar(COD) — (iii)
In ΔABD, AO is the median. ∴ar(AOD)=ar(AOB) — (iv)
From equations (i), (ii), (iii) and (iv), ar(BOC)=ar(COD)=ar(AOD)=ar(AOB)
So, the diagonals of a parallelogram divide it into four triangles of equal area.