Question

In tha figure bd= dc,pa=pd area of the triagle abc is 100sq.Cm
what is tha area of triangle pab

Answer 1

A median divides a Triangle into 2 triangles of equal areas.

It is given, BD=DC.

Therefore, AD is the median of ΔABC

⇒ ar.(ΔABD)=ar(ΔACD)

It is given, PA=PD

Therefore BP is the median of ΔABD

∴ ar(ΔBPD) = ar(ΔBPA)

⇒ar(ΔPAB) = 1÷2ar(ΔABD)

ar(ΔPAB) = 1/2ar(1/2ΔABC)     (∵ΔABD area is half of ΔABC(proved above))

∴ar(ΔPAB) = 1/4ar(ΔABC)

⇒ar(ΔPAB) = 1/4×100 (∵ ar(ΔABC) = 100cm²)

⇒ar(ΔPAB) = 25 cm²