Given:

DB = 20 cm

AB = 42 cm

AD = 34 cm

CD = 29 cm

CB = 21 cm

In ∆ABD(scalene),

Area of a scalene triangle = √(s(s-AB)(s-BD)(s-AD))

Where,

⇒ s = 48 cm

Now,

Area of a scalene triangle = √(48cm × (48-42)cm × (48-20)cm × (48-34)cm)

= √(48 cm × 6 cm × 28 cm × 14 cm)

= √112896 cm²

= 336 cm²

Similarly,

In ∆BCD (scalene),

Area of a scalene triangle = √(s(s-BC)(s-CD)(s-BD))

Where,

⇒ s = 35 cm

Now,

Area of a scalene triangle = √(35 cm × (35-29)cm × (35-20)cm × (35-21)cm)

= √(35 cm × 6 cm × 15 cm × 14 cm)

= √44100 cm²

= 210 cm²

Now,

Area of quadrilateral ABCD = Area of ∆ABD + Area of ∆BCD

= 336 cm² + 210 cm²

= 546 cm²