Question

In the given figure o is any point in the interior of parallelogram pqrs prove that ar of triangle poq+area of triangle sor=area of triangle pos+area of triangle qor =1/2area of parallelogram pqrs

Answer 1

const ab parallel to ps and qr.
now, ar(pos=1/2 pabs)......(1)
similarly, ar (qor=1/2baqr).........(2)
by adding eq 1 and 2 we get
ar(pos)+ar(qor)=1/2 ar(pabs)+ar(baqr)
hence,ar(pos)+ar(qor)=1/2ar(pqrs