ABCD is a trapezium in which AB I I DC. DC is produced to E such tha t CE= AB, prove that ar(`Delta`ABD) = ar(`Delta`BCE).

In figure, ABCD is a trapezium in which AB I I DC. Find the length of DC.

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

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

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

In the figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that ar( Delta AEDF) = ar( Delta ABCDE)

A point E is taken on the side BC of a parallelogram ABCD. AE and DC are produced to meet at F. Prove that ar(DeltaADF) = ar (ABFC) .

The base BC of Delta ABC is divided at D, so that BD=(1)/(2)DC. Prove that ar(Delta ABD)=(1)/(3)ar(Delta ABC)

In Fig.4.123, ABCD is a trapezium with AB||DC. If Delta AED is similar to Delta BEC, prove that AD=BC .

In the given figure, Here, ABCD is a parallellogram in which DC is extended to F such that AF intersects BC at E. Perimeter of Delta ABE =

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