Parallelograms on the Same Base and between the Same Parallels

In the figure, if parallelogram $PQFE$ and rectangle $PQRS$ are of equal area, then which of the following is true?

In the given figure, $ABCD$ and $ABPQ$ are two parallelograms and $M$ is a point on $AQ$ and $BMP$ is a triangle. Then, $ar(△BMP)=\frac{1}{2}ar( \square ABCD)$ is 

In the figure, if parallelogram $PQFE$ and rectangle $PQRS$ are of equal area, then which of the following is true?

In figure shown below, M and N are the mid points of the sides DC and AB of the parallelogram ABCD and the area of $\parallel$gm ABCD is $36 {\mathrm{cm}}^2.$
Write the area of $△BEC$

In figure shown below, the area of $\parallel$gm ABCD is $90$ ${\mathrm{cm}}^2$ and $AF\parallel BE$, find area (BEF)

In figure shown below, the area of $\parallel$gm $ABCD$ is $90$ ${\mathrm{cm}}^2$ and $AF\parallel BE$, find area $△ABD$.

In the figure shown below, the area of $\parallel$gm ABCD is $90$ ${\mathrm{cm}}^2$ and $AF\parallel BE$, find area (ABEF)

The area of a parallelogram is $390 {\mathrm{cm}}^2$ and height is $26 \mathrm{cm}$. If the length of the base of the parallelogram is $k \mathrm{cm}$, then find the value of $k$.

In Figure below, ABCD is a parallelogram. $BE\perp DC$ and $BF\perp AD$. If$AB=$$8$ cm, $BE=$$6$ cm and $BF=$$6.4$ cm, find AD. 

A triangle and a parallelogram each have a base of $5$ cm and area $50$ ${\mathrm{cm}}^2$. Calculate the ratio of their heights. 

Find the height of a parallelogram whose area is $50$${\mathrm{cm}}^2$ and whose base is$12.5 \mathrm{cm}$.

In figure shown below, $PR\parallel AD\parallel BC$ and $DC\parallel SQ\parallel AB$. Prove that area of quad $ABCD=$ $2$ area of quad $PQRS$.

In figure shown below, ABCD and AEFG are two parallelograms. Prove that area of $\parallel \mathrm{gm} ABCD=$area of $\parallel \mathrm{gm} AEFG$. 

$ABCD$ is a trapezium in which $AB\parallel DC$, $DC=30 \mathrm{cm}$ and $AB=50 \mathrm{cm}$. If $X$ and $Y$ are, respectively the mid points of $AD$ and $BC$, prove that area $DCXY$$=$$\frac{7}{9}$ area ($XYBA$).

In figure shown below, M and N are the mid points of the sides DC and AB of the parallelogram ABCD and the area of $\parallel$gm ABCD is $36 {\mathrm{cm}}^2$.
Name the $\parallel$gm which is equal in area to $△BEC$.

In figure $ABCD$ is a square and $APD$ is an equilateral triangle, Find $\angle PBC$and $\angle APB.$

In figure shown below, ABCD is a $\parallel \mathrm{gm}$. P is a point on BC such that BP:PC$=$$1:2$. DP produced meets AB produced at Q. If the area of $△CPQ=$$20$ ${\mathrm{cm}}^2$, calculate the area of $\parallel \mathrm{gm}$ ABCD and $△CDP$. 

In Figure shown below, $l$, $m$ and $n$ are straight lines such that $l\parallel m$ and $n$ intersects $l$ at $p$ and $m$ at $Q$. ABCD is a quadrilateral such that its vertex A is on $l$, the vertices C and D on m and $AD\parallel n$. Show that area$\left(ABCQ\right)=$area$\left(ABCDP\right)$.

In Figure shown below, ABCD is a trapezium with$BC\parallel AD$ and $\angle BAD=90°$. If the diagonals intersect at O, prove that area$\left( △ABO\right)=$area $\left(△OCD\right)$.

In Figure, ABCD is a rectangle and ABEF is a parallelogram, with same base AB and also have equal areas. Show that the perimeter of the parallelogram is greater than that of the rectangle.