Telangana Board Solutions for Chapter: Area and Perimeter, Exercise 4: Exercise - 2

Carefully study the following parallelograms.

Do parallelograms with equal bases and equal heights have the same area?   

The area of the following parallelogram is $k.76 {\mathrm{cm}}^2$. 

$\mathrm{PQRS}$ is a parallelogram. $\mathrm{PM}$ is the height from $\mathrm{P}$ to $\overline{\mathrm{SR}}$ and $\mathrm{PN}$ is the height from $\mathrm{P}$ to $\overline{\mathrm{QR}}$ . If $\mathrm{SR}=12 \mathrm{cm}$ and $\mathrm{PM}=7.6 \mathrm{cm}$. If the area of the parallelogram $\mathrm{PQRS}$ is $k {\mathrm{cm}}^2$, find the value of $k$.

$\mathrm{PQRS}$ is a parallelogram. $\mathrm{PM}$ is the height from $\mathrm{P}$ to $\overline{\mathrm{SR}}$ and $\mathrm{PN}$ is the height from $\mathrm{P}$ to $\overline{\mathrm{QR}}$ . If $\mathrm{SR}=12 \mathrm{cm}$ and $\mathrm{PM}=7.6 \mathrm{cm}$.

Find $\mathrm{PN}$ in $\mathrm{cm}$, if $\mathrm{QR}=8 \mathrm{cm}$.

$\mathrm{DF}$ and $\mathrm{BE}$ are the heights on sides $\mathrm{AB}$ and $\mathrm{AD}$ respectively in parallelogram $\mathrm{ABCD}$. If the area of the parallelogram is $1470 {\mathrm{cm}}^2$, $\mathrm{AB}=35 \mathrm{cm}$ and $\mathrm{AD}=49 \mathrm{cm}$, find the length of $\mathrm{BE}$ and $\mathrm{DF}$.

The height of a parallelogram is one-third of its base. If the area of the parallelogram is $192 {\mathrm{cm}}^2$, find its height and base.  

In a parallelogram the base and height are in the ratio of $5:2$. If the area of the parallelogram is $360 {\mathrm{m}}^2$, find its base and height.  

A square and a parallelogram have the same area. If a side of the square is $40 \mathrm{m}$ and the height of the parallelogram is $20 \mathrm{m}$, find the base of the parallelogram.