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ICSE Class X Math 2016 Solved Paper

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In the given figure PQRS is a cyclic quadrilateral PQ and SR produced meet at T.
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Question : 26
Total: 57
Find area of quadrilateral PQRS if area of △PTS=27cm2.
Solution:  
‌
‌ area of ‌∆TPS
‌ area of ‌∆TRQ
=‌‌
TP2
TR2

‌[∵∆TPS∼∆TRQ]
‌‌
27
‌ area of ‌∆TRQ
=‌
182
62

‌‌
27
‌ area of ‌∆TRQ
=‌
9
1

‌‌ area of ‌∆TRQ=3cm2
‌‌ area of quadrilateral ‌PQRS
‌‌=‌ area of ‌∆TPS−‌ area of ‌∆TQR
‌‌=27−3
‌‌=24cm2.
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