Find area of quadrilateral PQRS if area of \triangle P T S=27 {\cm}^2.

ICSE Class X Math 2016 Solved Paper - Question 26

In the given figure $P Q R S$ is a cyclic quadrilateral $P Q$ and $S R$ produced meet at $T$ .

Question : 26 of 57

Marks: +1, -0

Find area of quadrilateral PQRS if area of

△ P T S=27 {\cm}^2

Solution:

\;{\;\text " area of "\; ∆ {\TPS}}/{\;\text " area of "\; ∆ {\TRQ}}=\;\;{ {\TP}^2}/{ {\TR}^2}

\;{[ ∵ ∆ {\TPS} ∼ ∆ {\TRQ}] }

\;\;{27}/{\;\text " area of "\; ∆ {\TRQ}}= \;{18^2}/{6^2}

\;\;{27}/{\;\text " area of "\; ∆ {\TRQ}}= \;{9}/{1}

\;\;\text " area of "\; ∆ {\TRQ}=3 {\cm}^2

\;\;\text " area of quadrilateral "\; {\PQRS}

\;\; =\;\text " area of "\; ∆ {\TPS}-\;\text " area of "\; ∆ {\TQR}

\;\; =27-3

\;\; =24 {\cm}^2 .

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