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.

Question

Philoid · Accepted Answer

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