Question

Calculate the area of the quadrilateral $PQRS$ shown in the adjoining figure, given that $PQ=8cm,RQ=17cm,\angle RPQ={90}^o,RS=6cm$ and $\angle PRS={90}^o$.

Answer 1

$\to$ In $△PQR,P{R}^2=P{Q}^2+Q{R}^2=8^2+{17}^2=64+289=353$

In $△PRS,P{R}^2=R{S}^2+P{S}^2\Rightarrow P{S}^2=353-36=317$

Now $ar\left(PQRS\right)=ar\left(△PQR\right)+ar\left(△PRS\right)=\frac{1}{2}(8\times 17+6\times \sqrt{317})$

$=68+3\sqrt{317}$