Find the area of the trapezium $PQRS$ with height $PQ$ given in the figure (in $m^2$).

An isosceles right triangle has an area of $8 \, cm^{2}$. The length of its hypotenuse is

Write True or False and justify your answer.
If the side of a rhombus is $10 \, cm$ and one diagonal is $16 \, cm$,the area of the rhombus is $96 \, cm^2$.

For a triangle,$a = 15 \, cm$,$b = 20 \, cm$ and $s = 31 \, cm$,find the value of $c$.

For a rhombus plot,its perimeter is $680 \, m$ and one of its diagonals is $300 \, m$. Find the area of the plot. (in $, m^2$)

$A$ rectangular plot is given for constructing a house, having a measurement of $40 \, m$ long and $15 \, m$ in the front. According to the laws, a minimum of $3 \, m$ wide space should be left in the front and back each, and $2 \, m$ wide space on each of the other sides. Find the largest area where the house can be constructed (in $m^2$).