The parallel sides of a trapezium are $12 \mathrm{cm}$ and $36 \mathrm{cm}$. Its non-parallel sides are equal each being $15 \mathrm{cm}$. The area of the trapezium is $k {\mathrm{cm}}^2$. Find $k$.

The length one of the diagonal of a field in the form of a quadrilateral is $42 \mathrm{m}$. The perpendicular distance of the other two vertices from this diagonal are $12 \mathrm{cm}$ and $9 \mathrm{m} ($as shown in figure). The area of the field is $k {\mathrm{cm}}^2$. Find $k$.

In figure, the measurements are given on the figure itself. The area of quadrilateral $\mathrm{ABCD}$ is $k {\mathrm{cm}}^2$. Find $k$.

The area of the given figure $\mathrm{ABCDEFG}$ is $k {\mathrm{cm}}^2$. Find $k$.

The given figure is a pentagonal field which is ploughed at rate of $₹5.50 \mathrm{per} {\mathrm{m}}^2$. Find the cost of ploughing it if $\mathrm{AH}=120 \mathrm{m}, \mathrm{AF}=80 \mathrm{m}, \mathrm{AG}=50 \mathrm{m}, \mathrm{HC}=30 \mathrm{m}, \mathrm{BF}=50 \mathrm{m}, \mathrm{EG}=30 \mathrm{m}$ and $\mathrm{HD}=20 \mathrm{m}$.

Find the area of pentagon $\mathrm{ABCDE} ($see figure) in which $\mathrm{BF}\perp \mathrm{AC}, \mathrm{CG}\perp \mathrm{AD}$ and $\mathrm{EH}\perp \mathrm{AD}$ such that $\mathrm{AC}=8 \mathrm{cm}, \mathrm{AD}=15 \mathrm{cm}, \mathrm{BF}=3 \mathrm{cm}, \mathrm{CG}=7 \mathrm{cm}$ and $\mathrm{EH}=5 \mathrm{cm}$.