In the adjoining figure, ABCD is a quadrilateral. A line through D, parallel to AC, meets BC produced in P. then ar(△ABP)=ar(quad ABCD).

ABCD is a parallelogram in which BC is Produced to P such that CP=BC , as shown in the adjoining figure AP intersects CD at M. If ar(DMB) =7cm 2 find the area of parallelogram ABCD.

In parallelogram ABCD any point E is taken on the side BC. AE and DC when produced to meet at a point M. then ar(△ADM) = ar(ABMC).

In the adjoining figure, ABCD and BQSC are two parallelograms. then ar(△RSC)=ar(△PQB) .

M is the midpoint of the side AB of a parallelogram ABCD. If ar(AMCD)=24 cm², find ar(△ABC).

Calculate the area of Trapezium. PQRS given in figure.

In the adjoining figure, ABCD is a trapezium in which AB∣∣DC;AB=7 cm;AD=BC=5 cm and the distance between AB and DC is 4 cm. Find the length of DC and hence, find the area of trap. ABCD.

In the adjoining figure, CE∣∣AD and CF∣∣BA. then ar(△CBG)=ar(△AFG).

Show that a diagonal divides a parallelogram into two triangles of equal area

The abse BC of △ABC is divided at D such that BD= $\displaystyle \dfrac{1}{2}$ DC. then ar(△)=$\displaystyle \dfrac{1}{3}$×ar(△ABC).

Find the area of a trapezium whose parallel sides are 9 cm and 6 cm respectively and the distance between these sides is 8 cm.

BD is one of the diagonals of a quad, ABCD. If AL⊥BD and CM⊥BD, then (□ ABCD)=$\displaystyle \dfrac{1}{2}$ × BD×(AL+CM).

The vertex A of △ABC is joined to point D on the side BC. The midpoint of AD is E. then ar(△BEC)= $\displaystyle \dfrac{1}{2}$  ar(△ABC)

D is the midpoint of BC of △ABC and E is the midpoint of BD. If O is the midpoint of AE, then ar(△BOE)= $\displaystyle \dfrac{1}{2}$  ar(△ABC).

In a triangle ABC, the medians BE and CF intersect at G. Then ar(△BCG)=ar(AFGE).

In the adjoining figure, the diagonals AC and BD of a quadrilateral ABCD intersect at O. If BO=OD, then ar(△ABC)=ar(△ADC)

In figure, ABC and ABD are two triangles on the same base AB. If line-segment CD is bisected by AB at O, Then ar (ABC) = ar (ABD).

If P and Q are any two points lying respectively on the sides DC and AD of a parallelogram ABCD then ar(△APB)=ar(△BQC)

In the adjoining figure, △ABC and △ DBC are on the same base BC with A and D on opposite sides of BC such that ar(△ABC)=ar(△DBC). then BC bisects AD.

In the adjoining figure, show that ABCD is parallelogram. Calculate the area of parallelogram ABCD.

In the adjoining figure, D and E are respectively the mid point of sides AB and AC of △ABC. If PQ∣∣BC and CDP and BEQ are straight lines then ar(△ABQ)=ar(△ACP).

In the adjoining figure, ABCD is a trapezium in which AB∣∣DC and its diagonals AC and BD intersect at O.then ar(△AOD)=ar(△BOC).

In the adjoining figure, MNPQ and ABPQ are parallelogram and T is any point on the side BP. then ar(△ATQ)=1/2ar(MNPQ).

In the adjoining figure, DE∣∣BC. then ar(△ACD)=ar(△ABE)

In the adjoining figure, ABCD is a quadrilateral in which diag BD=14 cm. If AL⊥BD and CM⊥BD such that AL=8 cm and CM=6 cm, find the area of □ABCD.