In the following figure, quadrilaterals $\mathrm{ABDC}$ and $\mathrm{APQC}$ are concyclic ones. If $\mathrm{AB}$ and $\mathrm{CD}$ are two parallel lines, then $\mathrm{PBDQ}$ is necessary -

In the following figure, the only reflex angle of the dart is $216°$ and the second largest angle is $72°$. If each of the two smaller sides is $1 \mathrm{cm}$ and each of the two larger sides is $\frac{(1+\sqrt{5})}{2}$, find the area of the dart, in sq. $\mathrm{cm}$.

In the following quadrilateral $\mathrm{ABCD}$, the four mid-points $\mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{S}$ are joined in such a way that the quadrilateral is divided into six parts.

The ratio of the quadrilaterals  $\square \mathrm{ASOP}$$\square \mathrm{POQB}$, $\square \mathrm{OORCQ}$ $\square$$\mathrm{SDRO}$ is $4: 5: 7: 6$ and the ratio of $∆\mathrm{ASP}$ and $∆\mathrm{RCQ}$ is $2: 5$. If $S$ is joined to $R$ and $P$ is joined to$Q$, find the ratio of $\square \mathrm{PQRS}$ and $\square \mathrm{ABCD}.$