Question

PQTS and PTRQ are two parallelograms . show that ar (∆PST) = ar (∆QTR)= 1 by 3 ar (PQRS)

Answer 1

Hey friend

GIVEN:parallelograms PSTQ and parallelogram PQRT.
TO PROVE:ar(PST)=ar(QTR)=1/3*ar(PQRS)
SOLUTION:
ar(||gm PSTQ)=ar(||gm PQTR)
•Since both the ||gms are on the same base and between the same ||'s.

Now,
In ||gm PQTS
ar(PTS)=ar(PQT)-1
•diagonal of a ||gm dived it into 2 triangles.
Similarly,
In ||gm PQTR
ar(PQT)=ar(QRT) -2
=> by 1 & 2
ar(PTS)=ar(PQT)=ar(QTR)
=ar(PQRS)
ar(PTS)=1/3ar(PQRS)
SO....
ar(PTS)=ar(QTR)=1/3ar(PQRS)



HOPE THIS WILL HELP U!