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Question
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.
Solution
Parallelogram ABCD is made up of congruent `ΔABC and ΔADC`
Area of triangle ABC= `sqrt (s (s-a)(s-b)(s-c))`
Thus, we have :
`s=(a+b+c)/2`
`s=(34+20+42)/2`
`s=48 cm`
Area of Δ ABC=`sqrt(48(48-34)(48-20)(48-42))`
=`sqrt(48xx14xx28xx6)`
=`336 cm^2`
Now,
Area of the parallelogram=`2xx `Area of ΔABC
=`2xx336`
=`672 cm^2`
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