Given:

AB = 34 cm

BC = 20 cm

AC = 42 cm

The diagonal of a parallelogram divides it into two equal triangles.

Therefore,

Area of ABCD = 2 × Area of ∆ABC

Now,

We know that,

Area of a scalene triangle = √(s(s-AC)(s-AB)(s-BC))

Where,

⇒ s = 48cm

Now,

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

= √(48cm × 6cm × 14cm × 28cm)

= √112896 cm²

= 336 cm²

Therefore,

Area of ABCD = 2 × 336 cm²

= 672 cm²