Question

In the given figure $PQRS$ is a cyclic quadrilateral $PQ$ and $SR$ produced meet at $T$. Find area of quadrilateral $PQRS$ if area of $△PTS=27c{m}^2$ (given Triangle TPS is similar to TRQ)

Answer 1

$\frac{\text{area of triangle}TPS}{\text{area of triangle}TRQ}=\frac{T{P}^2}{T{R}^2}[\because △TPS\sim △TRQ]$
$\frac{27}{\text{area of triangle}TRQ}=\frac{{18}^2}{6^2}$
$\frac{27}{\text{area of triangle}TRQ}=\frac{9}{1}$
$\text{area of triangle}TRQ=3c{m}^2$
$\therefore \text{area of quadrilateral}PQRS=\text{area of triangle}TPS-\text{area of triangle}TRQ$
$=27-3$
$=24c{m}^2$