Question

PQTS and PTRQ are two parallelogram. Show that area(triangle PST)=area (triangle PQT)= area(triangleQPR)=1/3area(PQRS).

Answer 1

first prove that diagonal PT of Parallelogram PQTS divides it into two congruent triangles.
∴ΔPST congruent to ΔPQT
Similarly we can prove that
ΔPQT congruent to ΔQRT
we get that ΔPQT,ΔPST and ΔQRT are congruent 
∴ar(PQT)=ar(PST)=ar(QRT)
ar(PQRS)=ar(PQT)+ar(PST)+ar(QRT)
∴ar(PQRS)=3{ar(PQT)}=3{ar(PST)}=3{ar(QRT)}
∴ar(PQT)=ar(PST)=ar(QRT)=1/3 ar(PQRS)