In the figure , AP || BQ || CR. Prove that ar `(DeltaAQC)` = ar `(DeltaPBR)` .

In the figure, if ar DeltaRAS = ar DeltaRBS and [ar (DeltaQRB) = ar(DeltaPAS) then show that both the quadrilaterals PQSR and RSBA are trapeziums.

Triangle ABC and parallelogram ABEF are on the same base, AB as in between the same parallels AB and EF. Prove that ar (DeltaABC) = 1/2 ar(|| gm ABEF)

Delta ABC and Delta BDC are on the same base BC. Prove that (ar(Delta ABC))/(ar(Delta DBC)) =(AO)/(DO)

In the figure given below, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O , show that (ar(Delta ABC))/(ar(Delta DBC)) = (AO)/(DO) .

The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed . Show that ar (ABCD) = ar (PBQR)

In the trapezium ABCD, AB || CD , AB = 2 CD and ar(Delta AOB) = 84 cm^(2) , find the area of Delta COD .

Diagonals AC and BD of a trapezium ABCD with AB |\| DC intersect each other at O. Prove that ar (AOD) = ar (BOC).

In the figure 11.23, E is any point on median AD of a Delta ABC. Show that ar (ABE) = ar (ACE).

ABCD is a trapezium with AB || DC,. A line parallel to AC interseets AB at X and BC at Y. Prove that ar (ADX) = ar (ACY)