Question

Compute the area of trapezium PQRS is Fig. below.

Answer 1

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