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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.

A
672 cm2
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B
772 cm2
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C
336 cm2
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D
1008 cm2
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Solution

The correct option is A 672 cm2

In ||gm ABCD, AB = 34 cm, BC = 20 cm,
and AC = 42 cm.


Consider △ABC.
s=a+b+c2=34+20+422=962=48Area=s(sa)(sb)(sc)=48(4834)(4820)(4842)=48×14×28×6=7×4×3×2×2=336 cm2

The diagonal of a parallelogram divides it into two triangles of equal area.
Area of ||gm ABCD = 2×area of triangle ABC=2×336 cm2=672 cm2


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