In the given figure, a point D is taken on side BC of ΔABC and AD is produced to E, making DE = AD. Show that :
ar (ΔBEC) = ar (ΔABC).

Since, AD = DE thus, D is the mid-point of AE.

Median BD divides ΔABE into two Δs of equal area.

ar (ΔABD) = ar (ΔEBD) ….(1)

Median CD divides ΔACE into two Δs of equal area.

ar (ΔACD) = ar (ΔECD) ….(2)

Adding the Equations:

ar (ΔABD) + ar (ΔACD) = ar (ΔEBD) + ar (ΔECD)

∴ ar (ΔABC) = ar (ΔBEC)

Hence, proved that ar (ΔBEC) = ar (ΔABC).