Given

AD = 9 cm

BC = 8 cm

DC = 17 cm

Here Area of Quad ABCD = Area of ABD + Area of BCD

= x AB x AD + x BC x BD

By Pythagoras theorem in BCD

DC² = BD² + BC²

17² = BD² + 8²

BD² = 17² - 8² = 289 – 64 = 225

BD = 15 cm

Similarly in ABD using Pythagoras theorem

BD² = AD² + AB²

15² = 9² + AB²

AB² = 15 ² - 9² = 225 – 81 = 144

AB = 12 cm

Now, Area of Quad ABCD = Area of ABD + Area of BCD

= x AB x AD + x BC x BD

= x 12 x 9 + x 8 x 15 = 54 + 60 = 114 cm²

Area of Quadrilateral ABCD = 114 cm²