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)

Hope the answer is hepful !!

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