Question

P and Q are any two points on the diagonal AC of ||gm ABCD .Show that ar(∆PDQ)=ar(∆PBQ)​

Answer 1

$\huge{\pink {\sf\underline{Solution}}}$

Let, perpendicular from D and B on AC.

Since height will be h1 and h2 respectively.

We know,

ar (∆ADC) = ar (∆ABC)

$\frac{1}{2} </strong><strong>AC</strong><strong> \times h_{1} = \frac{1}{2}</strong><strong>AC</strong><strong> \times h_{2}$

So, h1 = h2

ar (∆APD) = 1/2 AP * h1

ar (∆ABP) = 1/2 AP * h2

Hence, ar (∆ADP) = ar (∆ABP)