O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Exercise 1: Exercise

Construct a parallelogram $ABCD$ and  parallelogram $ABEF$, where $AB=8 \mathrm{cm}$ and the altitude of each parallelogram is $3 \mathrm{cm}$. 

In figure, $AR=RC$ and $PC$ is parallel to $BQ$. Name a triangle equal to $△PCQ$ and a triangle equal in area to $△QPR$, giving your reason. Hence prove that areas of $△QPR$ and the quadrilateral $PBCR$ are equal.

$ABCD$ is a parallelogram and $E$ is any point on $AB$. If $DE$ is produced meets $CB$ produced at $F$, prove that the area of triangle $ADF=$ area of $∆DEC$.

$\mathrm{ABCD}$ is a parallelogram and $\mathrm{E}$ is any point on $\mathrm{AB}$. If $\mathrm{DE}$ is produced meets $\mathrm{CB}$ produced at $\mathrm{F}$, prove that the area of triangle $\mathrm{AEF}=$ area of triangle$\mathrm{BEC}$.

Prove that the parallelogram formed by joining the midpoints of the adjacent sides of a quadrilateral is half of the latter.

In figure, $AB\parallel DC\parallel EF, AD\parallel BC$ and $ED\parallel FA$. Prove that the area of $DEFH$is equal to the area of $ABCD$.

In the given figure,$\mathrm{M}$and $\mathrm{N}$are the midpoints of the sides$\mathrm{DC}$ and $\mathrm{AB}$ of the parallelogram $\mathrm{ABCD}$ and area of the parallelogram $\mathrm{ABCD}$ is $36 {\mathrm{cm}}^2$.

If the area of the triangle $\mathrm{BEC}$ is $k c{m}^2$ then find the value of $k$.

In the given figure,$\mathrm{M}$and $\mathrm{N}$are the midpoints of the sides$\mathrm{DC}$ and $\mathrm{AB}$ of the parallelogram $\mathrm{ABCD}$ and area of the parallelogram $\mathrm{ABCD}$ is $36 {\mathrm{cm}}^2$.

Name the parallelogram which is equal in area to the triangle $\mathrm{BEC}$.