Answer :

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


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