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

Write True or False and justify your answer.
The area of a triangle with base $4 \, \text{cm}$ and height $6 \, \text{cm}$ is $24 \, \text{cm}^2$.

The area of an isosceles triangle having base $2 \, cm$ and the length of one of the equal sides $4 \, cm$ is

$A$ 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 $\operatorname{Rs}$).

The perimeter of a triangular field is $420\, m$ and its sides are in the ratio $6: 7: 8$. Find the area of the triangular field (in $m^2$).

State whether the following statement is True or False and justify your answer:
The area of $\Delta ABC$ is $8 \, cm^2$ in which $AB = AC = 4 \, cm$ and $\angle A = 90^{\circ}$.