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

Does the following figure lie on the same base and between the same parallels? In such a case, write the common base and two parallels.

P,Q,R,S are respectively the midpoints of the sides AB,BC,CD and DA of parallelogram ABCD. Show that PQRS is a parallelogram and also show that ar(∣∣gm PQRS)= $\displaystyle \dfrac{1}{2}$ × ar(∣∣gm ABCD).

In a parallelogram ABCD, it being that AB=10 cm and the altitudes corresponding to the sides AB and AD ate DL=6 cm and BM=8 cm, respectively. Find AD.

In a trapezium ABCD, AB∣∣DC and M is the midpoint of BC. Through M a line PQ∣∣AD has been drawn meets AB in P and DC produced in Q, as shown in the adjoining figure. then ar(ABCD)=ar(APQD).

In the adjoining figure, BD∣∣CA,E is the midpoint of CA and BD= $\displaystyle \dfrac{1}{2}$  CA. Prove that ar(△ABC)=2 ar(△DBC).

Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and the two parallels

In the given Figure, ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.

If E,F,G and H are respectively the mid-points of the sides of a parallelogram ABCD, show that ar(EFGH)=$\displaystyle \dfrac{1}{2}$  ar(ABCD)

P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. then area (ΔAPB) = area(ΔBQC)

A farmer was having a field in the form of a parallelogram PQRS. She took any point A on RS and joined it to points P and Q. In how many parts the fields is divided? What are the shapes of these parts? The farmer wants to sow wheat and pulses in equal portions of the field separately. How should she do it?

In given figure,E is any point on median AD of a triangle ABC. then area(ABE)=area(ACE).

In a triangle ABC,E is the mid-point of median AD. then area(BED)= $\displaystyle \dfrac{1}{4}$  area(ABC).

Show that the diagonals of a parallelogram divide it into four triangles of equal area.

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

In the given Figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that

D and E are points on sides AB and AC respectively of △ABC such that area(DBC)=area(EBC). Prove that DE∥BC

XY is a line parallel to side BC of a △ABC. If BE∥AC and CF∥AB meet XY at E and F, respectively.then

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 (see Fig.). then ar (ABCD) = ar (PBQR).

Diagonals AC and BD of a trapezium ABCD with ABparallelDC intersect each other at O. then ar(AOD)=ar(BOC)

PQRS is a square. T and U are respectively, the mid-points of PS and QR (Fig.). Find the area of ∆OTS, if PQ = 8 cm, where O is the point of intersection of TU and QS.

ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ (Fig.). If AQ intersects DC at P, then ar (BPC) = ar (DPQ). Triangles On The Same Base And Between The Same Parallels

In fig ABCD is a trapezium in which AB= 7 cm, AD = BC = 5 cm. DC = x cm, and distance between AB and DC is 4 cm.Find the value of x and area of trapezium ABCD.

ABCD is a parallelogram and Q is any point on side AD. If ar(△QBC)=10 cm² , find ar(△QAB)+ar(△QDC).

In the given figure, area (parallelogram ABCD)=48 cm² and FC∥AB. Find area of ∥gm ABEF.