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The adjacent sides of a parallelogram AB...

The adjacent sides of a parallelogram ABCD are AB = 34 cm, BC = 20 cm and diagonal AC = 42 cm. Find the area of the parallelogram.

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In `Delta`ABC, it is given that
a = BC = 20 cm, b = AC = 42 cm and c = AB = 34 cm.
`therefore" "s=(1)/(2)(20+42+34)cm=48cm`.
`therefore" "(s-a)=28cm, (s-b)=6cm and (s-c)=14cm`.
`therefore" ""area of" Delta ABC = sqrt(s(s-a)(s-b)(s-c))`
`=sqrt(48 xx 28 xx 6 xx 14)cm^(2) = (14 xx 24) cm^(2)`
`= 336 cm^(2)`
`therefore" ""area of" ||"gm ABCD" = 2 xx ("area of" Delta ABC)`
`=(2 xx 336)cm^(2) = 672 cm^(2)`.
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