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

For ΔABC, a = 34 cm b = 42 cm c = 20 cm

$therefore space space space straight s equals fraction numerator straight a plus straight b plus straight c over denominator 2 end fraction space equals fraction numerator 34 plus 42 plus 20 over denominator 2 end fraction equals 48 space cm$
∴ Area of ΔABC
$equals square root of straight s left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight b right parenthesis left parenthesis straight s minus straight c right parenthesis end root equals space square root of 48 left parenthesis 48 minus 34 right parenthesis left parenthesis 48 minus 42 right parenthesis left parenthesis 48 minus 20 right parenthesis end root equals space square root of 48 left parenthesis 14 right parenthesis left parenthesis 6 right parenthesis left parenthesis 28 right parenthesis end root equals space 336 space cm squared$

∴ Area of parallelogram ABCD
= 2 Area of triangle ABC
= 2 x 336 cm² = 672 cm²

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Statistics

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.

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