Given that,

DC = 17 cm

AD = 9 cm

And,

BC = 8 cm

In Δ BCD, we have

CD² = BD² + BC²

(17)² = BD² + (8)²

BD² = 289 – 64

=15

In Δ ABD, we have

BD² = AB² + AD²

(15)² = AB² + (9)²

AB² = 225 – 81

= 144

=12

Therefore,

Area of Quadrilateral ABCD = Area (Δ ABD) + Area (Δ BCD)

Area of quadrilateral ABCD = (12 × 9) + (8 × 17)

= 54 + 68

= 112 cm²