The parallel sides of a trapezium are $20 \mathrm{cm}$ and $10 \mathrm{cm}$. Its non-parallel sides are both equal, each being $13 \mathrm{cm}$. Find the area of the trapezium.

In the given figure, $ABCD$ is a trapezium in which $AB=9 \mathrm{cm}, AD=BC=6 \mathrm{cm}, DC=x \mathrm{cm}$, and distance between $AB$ and $DC$ is $2\sqrt{5} \mathrm{cm}$. The value of area of trapezium ABCD is $k\sqrt{5}$. Find the value of $k$.

In the given figure, $ABCD$ is a parallelogram, $O$ is any point on $AC$. $PQ\parallel AB$ and $LM\parallel AD$. Prove that $ar\left({\parallel }^{\mathrm{gm}}DLOP\right)=ar\left({\parallel }^{\mathrm{gm}}BMOQ\right)$.

In the given figure, $ABCD$ is a parallelogram and $GBEF$ is a rectangle. Find $x$ and $y$.

Consider a parallelogram $\mathrm{ABCD}$ in the figure given below. Find the value of $\mathrm{x}$ and $\mathrm{y}$.

If $\mathrm{PQRS}$ is a parallelogram, then $\mathrm{y}$ equals