$A$ rhombus-shaped sheet with a perimeter of $40 \, cm$ and one diagonal of $12 \, cm$ is painted on both sides at the rate of $Rs \, 5$ per $cm^2$. Find the cost of painting (in $Rs$).

$A$ park,in the shape of a quadrilateral $ABCD$,has $\angle C = 90^{\circ}$,$AB = 9 \, m$,$BC = 12 \, m$,$CD = 5 \, m$,and $AD = 8 \, m$. How much area does it occupy (in $, m^{2}$)?

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

State whether the following statement is True or False and justify your answer:
The area of a regular hexagon of side $a$ is the sum of the areas of the five equilateral triangles with side $a$.

The shape of a plot is a rhombus. Its perimeter is $340 \, m$ and one diagonal is $72 \, m$. Find its area. (in $, m^2$)

In a quadrilateral $ABCD$,$AB = 9 \, cm$,$BC = 40 \, cm$,$CD = 28 \, cm$,$DA = 15 \, cm$,and $\angle B = 90^{\circ}$. Find its area. (in $, cm^2$)