The sides of a triangle measure $12 \, cm$,$16 \, cm$,and $20 \, cm$. What is the area of the triangle in $cm^2$?

How much paper of each shade is needed to make a kite as shown in the figure,where $ABCD$ is a square with diagonal $44 \, cm$? (in $cm^2$)

Find the area of the trapezium $PQRS$ given in the figure.

Write True or False and justify your answer.
The cost of levelling the ground in the form of a triangle having the sides $51 \, m$,$37 \, m$,and $20 \, m$ at the rate of $Rs \, 3$ per $m^2$ is $Rs \, 918$.

Find the cost of laying grass in a triangular field of sides $50 \, m$,$65 \, m$,and $65 \, m$ at the rate of $Rs \, 7$ per $m^2$ (in $Rs$).

$A$ field is in the shape of a trapezium having parallel sides $90 \, m$ and $30 \, m$. These sides meet the third side at right angles. The length of the fourth side is $100 \, m$. If it costs $\operatorname{Rs} 4$ to plough $1 \, m^2$ of the field,find the total cost of ploughing the field (in $\operatorname{Rs}$).