In the given figure, PQRS is a quadrilateral. If QR = 18 cm and PS = 9 cm, then what is the area (in cm2) of quadrilateral PQRS?

Answer: Option C

QP and RS extended to M to make an equilateral ΔMQR.
∠SPM = 180° - 150° = 30°
In ΔMPS

PS = 9 (Given)
$$\begin{array}{rl}& \tan 30^{\circ }=\frac{\text{MS}}{\text{PS}}\\ & \frac{1}{\sqrt{3}}=\frac{\text{MS}}{9}\\ & \text{MS}=\frac{9}{\sqrt{3}}\\ & \text{MS}=3\sqrt{3}\end{array}$$
Area of quadrilateral PQRS = Area of Equilateral Δ (MQR) - Area of ΔMSP
$$\begin{array}{rl}& =\frac{\sqrt{3}}{4}\times {\left(18\right)}^2-\frac{1}{2}\times 9\times 3\sqrt{3}\\ & =\frac{\sqrt{3}}{4}\times 18\times 18-\frac{27\sqrt{3}}{2}\\ & =\frac{27\sqrt{3}}{2}\left[6-1\right]\\ & =\frac{135\sqrt{3}}{2}\text{ c}{\text{m}}^2\end{array}$$