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Question

# Adjacent sides of a parallelogram are 5 cm and 3.5 cm. One of its diagonals is 6.5 cm. Then what is the area of parallelogram?

A
83 cm2
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B
93 cm2
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C
103 cm2
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D
123 cm2
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Solution

## The correct option is C 10√3 cm2Given, ABCD is a parallelogram having AB=5 cm,BC=3.5 cm and one of the diagonal AC=6.5 cm.We know that the diagonal of a parallelogram divides it into two triangles of equal area.Therefore, in triangle ABC, by heron's formula, we have a=5 cm,b=3.5 cm and c=6.5 cm⟹semi−perimeteroftriangleABC,s=a+b+c2=5+3.5+6.52=7.5cm∴area of triangleABC=√s(s−a)(s−b)(s−c)=√7.5(7.5−5)(7.5−3.5)(7.5−6.5)=5√3 cm2⟹AreaofparallelogramABCD=2×areaoftriangleABC=2×5√3cm2=10√3 cm2.

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