If P is a point on the median AD of a ΔABC, then ar (ΔABP) = ar(ΔACP).
In ∆ABC,
Since, AD is the median
Thus, BD = DC
Let the height of ∆ABC be h
ar(∆ABD) = ar(∆ABD)
1/2 × h × BD = 1/2 × h × BD
1/2 × h × BD = 1/2 × h × CD
∴ ar (∆ABD) = ar (∆ADC)
Let H be the height of ∆BPD and ∆PDC
∴ ar (∆BPD) = ar (∆PDC)
Now, ar(∆ABD) = ar (∆ABP) + ar (∆BPD)
And, ar(∆ACD) = ar(∆ACP) + ar(∆PDC)
Thus, ar(∆ABP) = ar(∆ACP)
∴ Option A is correct