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Question

# Two adjacent sides of a parallelogram are 34 cm and 20cm. One of its diagonals is 42 cm. Then the area of the parallelogram is

A
612 sq.cm
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B
672 sq.cm
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C
784 sq.cm
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D
796 sq.cm
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Solution

## The correct option is B 672 sq.cmREF.imageArea of triangle = √S(S−a)(S−b)(S−c)( Here, S is the semi-perimeter)S=a+b+c2⇒S=42+20+342⇒S=962⇒S=48cmArea of ΔABC=√48(48−34)(48−20)(48−42)=√48×14×28×6=336 cm2Now,Area of parallelogram = 2× Area of ΔABC=2×336=627cm2∴ so, the answer is B. 672cm2 or 672 sq.cm

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