Q31 of 97 Page 780

The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.

Given:


AB = 34 cm


BC = 20 cm


AC = 42 cm


In ∆ABC (scalene),


Area of ∆ABC = √(s(s-AB)(s-BC)(s-AC))


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


Now,


Area of parallelogram ABCD = 2 × Area of ∆ABC


= 2 × 336 cm2


= 672 cm2


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