We have,

Area of trapezium PQRS = Area of rectangle PSRT + Area (Δ QRT)

Area of trapezium PQRS = PT * RT + (QT * RT)

= 8 * RT + (8 * RT)

= 12 * RT

In Δ QRT, we have

QR² = QT² + RT²

RT² = QR² - QT²

RT² = (17)² - (8)²

= 225

= 15

Hence,

Area of trapezium PQRS = 12 * 15

= 180 cm²