A field in the form of parallelogram has sides $60 \mathrm{m}$ and $40 \mathrm{m}$ and one of its diagonals is $80 \mathrm{m}$ long. Find the area of parallelogram.

A rhombus shaped sheet with perimeter $40 \mathrm{cm}$ and one diagonal $12 \mathrm{m}$, is painted on both sides at the rate of $Rs 5 \mathrm{per} {\mathrm{cm}}^2$. Find the cost of painting.

Find the area of the trapezium $PQRS$ with height $PQ$ given in the figure.

How much paper of each shade is needed to make a kite given in the figure, in which $\mathrm{ABCD}$ is square with diagonal $44 \mathrm{cm}$?

A rectangular plot is given for constructing a house having a measurement of $40 \mathrm{m}$ length and $15 \mathrm{m}$ in the front. According to the laws, a minimum of $3 \mathrm{m}$ wide space should be left in the front and back each and $2 \mathrm{m}$ wide space on each of other sides. If the largest area where the house can be constructed is $k {\mathrm{m}}^2$, find the value of $k$.