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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 cm2In ||gm ABCD, AB = 34 cm, BC = 20 cm, and AC = 42 cm. Consider △ABC. s=a+b+c2=34+20+422=962=48∴Area=√s(s−a)(s−b)(s−c)=√48(48−34)(48−20)(48−42)=√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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