Question

In the given figure, P is any point on the diagonal AC of the parallelogram ABCD. Show that ar(ΔADP) = ar (ΔABP).

Answer 1

Let, perpendicular from D and B on AC be h1 and h2 respectively.
We know, ar (ADC) = ar (ABC)
1/2 AC* h1 = 1/2 AC * h2
So, h1 = h2
ar (APD) = 1/2 AP * h1
ar (ABP) = 1/2 AP * h2
Hence, ar (ADP) = ar (ABP)