In figure, the area of the quadrilateral PQRS is

Area of Quadrilateral$=$ Area of $\Delta PQS$ $+$ Area of $\Delta SQR$

$\Delta PQS,S{Q}^2=P{Q}^2-P{S}^2$

${\left(26\right)}^2={\left(PQ\right)}^2-{\left(24\right)}^2$

$676={\left(PQ\right)}^2+576$

$676-576={\left(PQ\right)}^2$

$100=P{Q}^2\Rightarrow PQ=\sqrt{100}=10\text{ cm}$

$\Delta SQR,\frac{\sqrt{3}}{4}{a}^2=\frac{\sqrt{3}}{4}{\left(26\right)}^2=292.71{\text{ cm}}^2$

$\Delta PQR=\frac{1}{2}\times b\times h=\frac{1}{2}\times 10\times 24=120{\text{ cm}}^2$

$\therefore$ Area of Quadrilateral $=292.71{\text{ cm}}^2+120{\text{cm}}^2$

$=412.71{\text{cm}}^2$