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Question
Compute the area of trapezium PQRS is Fig. below.
Solution
We have
ar (trap PQRS) = ar (rect PSRT) + are a (ΔQRT)
⇒ ar (trap .PQRS) = PT × RT =`1/2`(QT × RT)
= `8 xx RT = 1/2 ( 8 xx RT ) = 12 xx RT `
In , ΔQRT , we have
QR2 = QT2 + RT2
⇒ RT 2 = QR2 - QT2
⇒ ( RT )2 = 172 - 8 2 = 225
⇒ RT = 15
Hence, ar (trap . PQRS ) = 12 × 15cm 2 = 180 cm2
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